Method and apparatus for coding image on basis of transform

ABSTRACT

An image decoding method according to the present document may comprise the steps of: deriving a first variable indicating whether there is a valid coefficient in a region excluding a DC region from a current block; deriving a second variable indicating whether there is a valid coefficient in a second region excluding a first region formed at the upper left end of the current block; when the first variable indicates that the valid coefficient exists in the region excluding the DC region, and the second variable indicates that the valid coefficient does not exist in the second region, parsing an LFNST index from the bitstream; and applying an LFNST matrix derived on the basis of the LFNST index to transform coefficients in the first region, to derive the modified transform coefficients.

TECHNICAL FIELD

The present disclosure relates to an image coding technique and, moreparticularly, to a method and an apparatus for coding an image based ontransform in an image coding system.

RELATED ART

Nowadays, the demand for high-resolution and high-quality images/videossuch as 4K, 8K or more ultra high definition (UHD) images/videos hasbeen increasing in various fields. As the image/video data becomeshigher resolution and higher quality, the transmitted information amountor bit amount increases as compared to the conventional image data.Therefore, when image data is transmitted using a medium such as aconventional wired/wireless broadband line or image/video data is storedusing an existing storage medium, the transmission cost and the storagecost thereof are increased.

Further, nowadays, the interest and demand for immersive media such asvirtual reality (VR), artificial reality (AR) content or hologram, orthe like is increasing, and broadcasting for images/videos having imagefeatures different from those of real images, such as a game image isincreasing.

Accordingly, there is a need for a highly efficient image/videocompression technique for effectively compressing and transmitting orstoring, and reproducing information of high resolution and high qualityimages/videos having various features as described above.

SUMMARY

A technical aspect of the present disclosure is to provide a method andan apparatus for increasing image coding efficiency.

Another technical aspect of the present disclosure is to provide amethod and an apparatus for increasing efficiency in transform indexcoding.

Still another technical aspect of the present disclosure is to providean image coding method and apparatus using LFNST.

Still another technical aspect of the present disclosure is to providean image coding method and apparatus for zero-out performed when LFNSTis applied.

According to an embodiment of the present disclosure, there is providedan image decoding method performed by a decoding apparatus. The methodmay include: obtaining residual information from a bitstream ; derivingtransform coefficients for a current block based on the residualinformation; deriving a first variable indicating whether a significantcoefficient exists in a region excluding a DC region of the currentblock; deriving a second variable indicating whether a significantcoefficient exists in a second region other than a first region at thetop-left of the current block; parsing an LFNST index from the bitstreamwhen the first variable indicates that the significant coefficientexists in the region excluding the DC region and the second variableindicates that the significant coefficient does not exist in the secondregion; deriving residual samples for the current block based on aninverse primary transform for the modified transform coefficients; andgenerating a reconstructed picture based on the residual samples for thecurrent block.

The first variable is derived as 0 when the index of a subblockincluding a last significant coefficient in the current block is 0 andthe position of the last significant coefficient in the subblock isgreater than 0, and the LFNST index is parsed when the first variable is0.

The LFNST index is parsed when the first variable is 0 the firstvariable is changed to 0 when the significant coefficient exists in theregion excluding the DC region.

The second variable is derived as 0 when the index of the sub-blockincluding the last significant coefficient in the current block isgreater than 0 and the width and height of the current block are 4 ormore, and the LFNST index is not parsed when the second variable is 0.

The second variable is derived as 0 when the size of the current blockis 4×4 or 8×8 and the position of the last significant coefficient isgreater than 7, and the LFNST index is not parsed when the secondvariable is 0.

The second variable is initially set to 1, and the second variable ischanged to 0 when the significant coefficient exists in the secondregion.

According to another embodiment of the present disclosure, there isprovided an image encoding method performed by an encoding apparatus.The method may include: deriving prediction samples for a current block;deriving residual samples for the current block based on the predictionsample; deriving transform coefficients for the current block based on aprimary transform for the residual samples; deriving modified transformcoefficients for the current block based on the transform coefficientsof a first region at the top-left of the current block and apredetermined LFNST matrix; zeroing out a second region of the currentblock in which the modified transform coefficients do not exist;constructing image information so that an LFNST index indicating theLFNST matrix is signaled when a significant coefficient exists in aregion excluding a DC region of the current block and the zeroing-out isperformed, and encoding the image information including residualinformation derived through quantization of the modified transformcoefficients and the LFNST index.

According to still another embodiment of the present disclosure, theremay be provided a digital storage medium that stores image dataincluding encoded image information and a bitstream generated accordingto an image encoding method performed by an encoding apparatus.

According to yet another embodiment of the present disclosure, there maybe provided a digital storage medium that stores image data includingencoded image information and a bitstream to cause a decoding apparatusto perform the image decoding method.

According to the present disclosure, it is possible to increase overallimage/video compression efficiency.

According to the present disclosure, it is possible to increaseefficiency in transform index coding.

A technical aspect of the present disclosure may provide an image codingmethod and apparatus using LFNST.

A technical aspect of the present disclosure may provide an image codingmethod and apparatus for zero-out performed when LFNST is applied.

The effects that can be obtained through specific examples of thepresent disclosure are not limited to the effects listed above. Forexample, there may be various technical effects that a person havingordinary skill in the related art can understand or derive from thepresent disclosure. Accordingly, specific effects of the presentdisclosure are not limited to those explicitly described in the presentdisclosure and may include various effects that can be understood orderived from the technical features of the present disclosure.

BRIEF DESCRIPTION OF THE DRAWINGS

FIG. 1 schematically illustrates an example of a video/image codingsystem to which the present disclosure is applicable.

FIG. 2 is a diagram schematically illustrating a configuration of avideo/image encoding apparatus to which the present disclosure isapplicable.

FIG. 3 is a diagram schematically illustrating a configuration of avideo/image decoding apparatus to which the present disclosure isapplicable.

FIG. 4 is schematically illustrates a multiple transform schemeaccording to an embodiment of the present document.

FIG. 5 exemplarily shows intra directional modes of 65 predictiondirections.

FIG. 6 is a diagram for explaining RST according to an embodiment of thepresent.

FIG. 7 is a diagram illustrating a sequence of arranging output data ofa forward primary transformation into a one-dimensional vector accordingto an example.

FIG. 8 is a diagram illustrating a sequence of arranging output data ofa forward secondary transform into a two-dimensional vector according toan example.

FIG. 9 is a diagram illustrating wide-angle intra prediction modesaccording to an embodiment of the present document.

FIG. 10 is a diagram illustrating a block shape to which LFNST isapplied.

FIG. 11 is a diagram illustrating an arrangement of output data of aforward LFNST according to an example.

FIG. 12 is a diagram illustrating that the number of output data for aforward LFNST is limited to a maximum of 16 according to an example.

FIG. 13 is a diagram illustrating zero-out in a block to which 4×4 LFNSTis applied according to an example.

FIG. 14 is a diagram illustrating zero-out in a block to which 8×8 LFNSTis applied according to an example.

FIG. 15 is a diagram illustrating zero-out in a block to which 8×8 LFNSTis applied according to another example.

FIG. 16 is a flowchart for explaining an image decoding method accordingto an example.

FIG. 17 is a flowchart for explaining an image encoding method accordingto an example.

FIG. 18 illustrates the structure of a content streaming system to whichthe present disclosure is applied.

DESCRIPTION OF EXEMPLARY EMBODIMENTS

While the present disclosure may be susceptible to various modificationsand include various embodiments, specific embodiments thereof have beenshown in the drawings by way of example and will now be described indetail. However, this is not intended to limit the present disclosure tothe specific embodiments disclosed herein. The terminology used hereinis for the purpose of describing specific embodiments only, and is notintended to limit technical idea of the present disclosure. The singularforms may include the plural forms unless the context clearly indicatesotherwise. The terms such as “include” and “have” are intended toindicate that features, numbers, steps, operations, elements,components, or combinations thereof used in the following descriptionexist, and thus should not be understood as that the possibility ofexistence or addition of one or more different features, numbers, steps,operations, elements, components, or combinations thereof is excluded inadvance.

Meanwhile, each component on the drawings described herein isillustrated independently for convenience of description as tocharacteristic functions different from each other, and however, it isnot meant that each component is realized by a separate hardware orsoftware. For example, any two or more of these components may becombined to form a single component, and any single component may bedivided into plural components. The embodiments in which components arecombined and/or divided will belong to the scope of the patent right ofthe present disclosure as long as they do not depart from the essence ofthe present disclosure.

Hereinafter, preferred embodiments of the present disclosure will beexplained in more detail while referring to the attached drawings. Inaddition, the same reference signs are used for the same components onthe drawings, and repeated descriptions for the same components will beomitted.

This document relates to video/image coding. For example, themethod/example disclosed in this document may relate to a VVC (VersatileVideo Coding) standard (ITU-T Rec. H.266), a next-generation video/imagecoding standard after VVC, or other video coding related standards (e.g., HEVC (High Efficiency Video Coding) standard (ITU-T Rec. H.265), EVC(essential video coding) standard, AVS2 standard, etc.).

In this document, a variety of embodiments relating to video/imagecoding may be provided, and, unless specified to the contrary, theembodiments may be combined to each other and be performed.

In this document, a video may mean a set of a series of images overtime. Generally a picture means a unit representing an image at aspecific time zone, and a slice/tile is a unit constituting a part ofthe picture. The slice/tile may include one or more coding tree units(CTUs). One picture may be constituted by one or more slices/tiles. Onepicture may be constituted by one or more tile groups. One tile groupmay include one or more tiles.

A pixel or a pel may mean a smallest unit constituting one picture (orimage). Also, ‘sample’ may be used as a term corresponding to a pixel. Asample may generally represent a pixel or a value of a pixel, and mayrepresent only a pixel/pixel value of a luma component or only apixel/pixel value of a chroma component. Alternatively, the sample mayrefer to a pixel value in the spatial domain, or when this pixel valueis converted to the frequency domain, it may refer to a transformcoefficient in the frequency domain.

A unit may represent the basic unit of image processing. The unit mayinclude at least one of a specific region and information related to theregion. One unit may include one luma block and two chroma (e.g., cb,cr) blocks. The unit and a term such as a block, an area, or the likemay be used in place of each other according to circumstances. In ageneral case, an M x N block may include a set (or an array) of samples(or sample arrays) or transform coefficients consisting of M columns andN rows.

In this document, the term “/” and “,” should be interpreted to indicate“and/or.” For instance, the expression “A/B” may mean “A and/or B.”Further, “A, B” may mean “A and/or B.” Further, “A/B/C” may mean “atleast one of A, B, and/or C.” Also, “A/B/C” may mean “at least one of A,B, and/or C.”

Further, in the document, the term “or” should be interpreted toindicate “and/or.” For instance, the expression “A or B” may include 1)only A, 2) only B, and/or 3) both A and B. In other words, the term “or”in this document should be interpreted to indicate “additionally oralternatively.”

In the present disclosure, “at least one of A and B” may mean “only A”,“only B”, or “both A and B”. In addition, in the present disclosure, theexpression “at least one of A or B” or “at least one of A and/or B” maybe interpreted as “at least one of A and B”.

In addition, in the present disclosure, “at least one of A, B, and C”may mean “only A”, “only B”, “only C”, or “any combination of A, B, andC”. In addition, “at least one of A, B, or C” or “at least one of A, B,and/or C” may mean “at least one of A, B, and C”.

In addition, a parenthesis used in the present disclosure may mean “forexample”. Specifically, when indicated as “prediction (intraprediction)”, it may mean that “intra prediction” is proposed as anexample of “prediction”. In other words, the “prediction” of the presentdisclosure is not limited to “intra prediction”, and “intra prediction”may be proposed as an example of “prediction”. In addition, whenindicated as “prediction (i.e., intra prediction)”, it may also meanthat “intra prediction” is proposed as an example of “prediction”.

Technical features individually described in one figure in the presentdisclosure may be individually implemented or may be simultaneouslyimplemented.

FIG. 1 schematically illustrates an example of a video/image codingsystem to which the present disclosure is applicable.

Referring to FIG. 1 , the video/image coding system may include a firstdevice (source device) and a second device (receive device). The sourcedevice may deliver encoded video/image information or data in the formof a file or streaming to the receive device via a digital storagemedium or network.

The source device may include a video source, an encoding apparatus, anda transmitter. The receive device may include a receiver, a decodingapparatus, and a renderer. The encoding apparatus may be called avideo/image encoding apparatus, and the decoding apparatus may be calleda video/image decoding apparatus. The transmitter may be included in theencoding apparatus. The receiver may be included in the decodingapparatus. The renderer may include a display, and the display may beconfigured as a separate device or an external component.

The video source may obtain a video/image through a process ofcapturing, synthesizing, or generating a video/image. The video sourcemay include a video/image capture device and/or a video/image generatingdevice. The video/image capture device may include, for example, one ormore cameras, video/image archives including previously capturedvideo/images, or the like. The video/image generating device mayinclude, for example, a computer, a tablet and a smartphone, and may(electronically) generate a video/image. For example, a virtualvideo/image may be generated through a computer or the like. In thiscase, the video/image capturing process may be replaced by a process ofgenerating related data.

The encoding apparatus may encode an input video/image. The encodingapparatus may perform a series of procedures such as prediction,transform, and quantization for compression and coding efficiency. Theencoded data (encoded video/image information) may be output in the formof a bitstream.

The transmitter may transmit the encoded video/image information or dataoutput in the form of a bitstream to the receiver of the receive devicethrough a digital storage medium or a network in the form of a file orstreaming. The digital storage medium may include various storagemediums such as USB, SD, CD, DVD, Blu-ray, HDD, SSD, and the like. Thetransmitter may include an element for generating a media file through apredetermined file format, and may include an element for transmissionthrough a broadcast/communication network. The receiver mayreceive/extract the bitstream and transmit the received/extractedbitstream to the decoding apparatus.

The decoding apparatus may decode a video/image by performing a seriesof procedures such as dequantization, inverse transform, prediction, andthe like corresponding to the operation of the encoding apparatus.

The renderer may render the decoded video/image. The renderedvideo/image may be displayed through the display.

FIG. 2 is a diagram schematically illustrating a configuration of avideo/image encoding apparatus to which the present disclosure isapplicable. Hereinafter, what is referred to as the video encodingapparatus may include an image encoding apparatus.

Referring to FIG. 2 , the encoding apparatus 200 may include an imagepartitioner 210, a predictor 220, a residual processor 230, an entropyencoder 240, an adder 250, a filter 260, and a memory 270. The predictor220 may include an inter predictor 221 and an intra predictor 222. Theresidual processor 230 may include a transformer 232, a quantizer 233, adequantizer 234, an inverse transformer 235. The residual processor 230may further include a subtractor 231. The adder 250 may be called areconstructor or reconstructed block generator. The image partitioner210, the predictor 220, the residual processor 230, the entropy encoder240, the adder 250, and the filter 260, which have been described above,may be constituted by one or more hardware components (e.g., encoderchipsets or processors) according to an embodiment. Further, the memory270 may include a decoded picture buffer (DPB), and may be constitutedby a digital storage medium. The hardware component may further includethe memory 270 as an internal/external component.

The image partitioner 210 may partition an input image (or a picture ora frame) input to the encoding apparatus 200 into one or more processingunits. As one example, the processing unit may be called a coding unit(CU). In this case, starting with a coding tree unit (CTU) or thelargest coding unit (LCU), the coding unit may be recursivelypartitioned according to the Quad-tree binary-tree ternary-tree (QTBTTT)structure. For example, one coding unit may be divided into a pluralityof coding units of a deeper depth based on the quad-tree structure, thebinary-tree structure, and/or the ternary structure. In this case, forexample, the quad-tree structure may be applied first and thebinary-tree structure and/or the ternary structure may be applied later.Alternatively, the binary-tree structure may be applied first. Thecoding procedure according to the present disclosure may be performedbased on the final coding unit which is not further partitioned. In thiscase, the maximum coding unit may be used directly as a final codingunit based on coding efficiency according to the image characteristic.Alternatively, the coding unit may be recursively partitioned intocoding units of a further deeper depth as needed, so that the codingunit of an optimal size may be used as a final coding unit. Here, thecoding procedure may include procedures such as prediction, transform,and reconstruction, which will be described later. As another example,the processing unit may further include a prediction unit (PU) or atransform unit (TU). In this case, the prediction unit and the transformunit may be split or partitioned from the above-described final codingunit. The prediction unit may be a unit of sample prediction, and thetransform unit may be a unit for deriving a transform coefficient and/ora unit for deriving a residual signal from a transform coefficient.

The unit and a term such as a block, an area, or the like may be used inplace of each other according to circumstances. In a general case, anM×N block may represent a set of samples or transform coefficientsconsisting of M columns and N rows. The sample may generally represent apixel or a value of a pixel, and may represent only a pixel/pixel valueof a luma component, or only a pixel/pixel value of a chroma component.The sample may be used as a term corresponding to a pixel or a pel ofone picture (or image).

The subtractor 231 subtractes a prediction signal (predicted block,prediction sample array) output from the predictor 220 from an inputimage signal (original block, original sample array) to generate aresidual signal (residual block, residual sample array), and thegenerated residual signal is transmitted to the transformer 232. Thepredictor 220 may perform prediction on a processing target block(hereinafter, referred to as ‘current block’), and may generate apredicted block including prediction samples for the current block. Thepredictor 220 may determine whether intra prediction or inter predictionis applied on a current block or CU basis. As discussed later in thedescription of each prediction mode, the predictor may generate variousinformation relating to prediction, such as prediction mode information,and transmit the generated information to the entropy encoder 240. Theinformation on the prediction may be encoded in the entropy encoder 240and output in the form of a bitstream.

The intra predictor 222 may predict the current block by referring tosamples in the current picture. The referred samples may be located inthe neighbor of or apart from the current block according to theprediction mode. In the intra prediction, prediction modes may include aplurality of non-directional modes and a plurality of directional modes.The non-directional modes may include, for example, a DC mode and aplanar mode. The directional mode may include, for example, 33directional prediction modes or 65 directional prediction modesaccording to the degree of detail of the prediction direction. However,this is merely an example, and more or less directional prediction modesmay be used depending on a setting. The intra predictor 222 maydetermine the prediction mode applied to the current block by using theprediction mode applied to the neighboring block.

The inter predictor 221 may derive a predicted block for the currentblock based on a reference block (reference sample array) specified by amotion vector on a reference picture. At this time, in order to reducethe amount of motion information transmitted in the inter predictionmode, the motion information may be predicted on a block, subblock, orsample basis based on correlation of motion information between theneighboring block and the current block. The motion information mayinclude a motion vector and a reference picture index. The motioninformation may further include inter prediction direction (L0prediction, L1 prediction, Bi prediction, etc.) information. In the caseof inter prediction, the neighboring block may include a spatialneighboring block existing in the current picture and a temporalneighboring block existing in the reference picture. The referencepicture including the reference block and the reference pictureincluding the temporal neighboring block may be same to each other ordifferent from each other. The temporal neighboring block may be calleda collocated reference block, a collocated CU (colCU), and the like, andthe reference picture including the temporal neighboring block may becalled a collocated picture (colPic). For example, the inter predictor221 may configure a motion information candidate list based onneighboring blocks and generate information indicating which candidateis used to derive a motion vector and/or a reference picture index ofthe current block. Inter prediction may be performed based on variousprediction modes. For example, in the case of a skip mode and a mergemode, the inter predictor 221 may use motion information of theneighboring block as motion information of the current block. In theskip mode, unlike the merge mode, the residual signal may not betransmitted. In the case of the motion information prediction (motionvector prediction, MVP) mode, the motion vector of the neighboring blockmay be used as a motion vector predictor and the motion vector of thecurrent block may be indicated by signaling a motion vector difference.

The predictor 220 may generate a prediction signal based on variousprediction methods. For example, the predictor may apply intraprediction or inter prediction for prediction on one block, and, aswell, may apply intra prediction and inter prediction at the same time.This may be called combined inter and intra prediction (CIIP). Further,the predictor may be based on an intra block copy (IBC) prediction mode,or a palette mode in order to perform prediction on a block. The IBCprediction mode or palette mode may be used for content image/videocoding of a game or the like, such as screen content coding (SCC).Although the IBC basically performs prediction in a current block, itcan be performed similarly to inter prediction in that it derives areference block in a current block. That is, the IBC may use at leastone of inter prediction techniques described in the present disclosure.

The prediction signal generated through the inter predictor 221 and/orthe intra predictor 222 may be used to generate a reconstructed signalor to generate a residual signal. The transformer 232 may generatetransform coefficients by applying a transform technique to the residualsignal. For example, the transform technique may include at least one ofa discrete cosine transform (DCT), a discrete sine transform (DST), aKarhunen-Loève transform (KLT), a graph-based transform (GBT), or aconditionally non-linear transform (CNT). Here, the GBT means transformobtained from a graph when relationship information between pixels isrepresented by the graph. The CNT refers to transform obtained based ona prediction signal generated using all previously reconstructed pixels.In addition, the transform process may be applied to square pixel blockshaving the same size or may be applied to blocks having a variable sizerather than the square one.

The quantizer 233 may quantize the transform coefficients and transmitthem to the entropy encoder 240, and the entropy encoder 240 may encodethe quantized signal (information on the quantized transformcoefficients) and output the encoded signal in a bitstream. Theinformation on the quantized transform coefficients may be referred toas residual information. The quantizer 233 may rearrange block typequantized transform coefficients into a one-dimensional vector formbased on a coefficient scan order, and generate information on thequantized transform coefficients based on the quantized transformcoefficients of the one-dimensional vector form. The entropy encoder 240may perform various encoding methods such as, for example, exponentialGolomb, context-adaptive variable length coding (CAVLC),context-adaptive binary arithmetic coding (CABAC), and the like. Theentropy encoder 240 may encode information necessary for video/imagereconstruction other than quantized transform coefficients (e.g. valuesof syntax elements, etc.) together or separately. Encoded information(e.g., encoded video/image information) may be transmitted or stored ona unit basis of a network abstraction layer (NAL) in the form of abitstream. The video/image information may further include informationon various parameter sets such as an adaptation parameter set (APS), apicture parameter set (PPS), a sequence parameter set (SPS), a videoparameter set (VPS) or the like. Further, the video/image informationmay further include general constraint information. In the presentdisclosure, information and/or syntax elements which aretransmitted/signaled to the decoding apparatus from the encodingapparatus may be included in video/image information. The video/imageinformation may be encoded through the above-described encodingprocedure and included in the bitstream. The bitstream may betransmitted through a network, or stored in a digital storage medium.Here, the network may include a broadcast network, a communicationnetwork and/or the like, and the digital storage medium may includevarious storage media such as USB, SD, CD, DVD, Blu-ray, HDD, SSD, andthe like. A transmitter (not shown) which transmits a signal output fromthe entropy encoder 240 and/or a storage (not shown) which stores it maybe configured as an internal/external element of the encoding apparatus200, or the transmitter may be included in the entropy encoder 240.

Quantized transform coefficients output from the quantizer 233 may beused to generate a prediction signal. For example, by applyingdequantization and inverse transform to quantized transform coefficientsthrough the dequantizer 234 and the inverse transformer 235, theresidual signal (residual block or residual samples) may bereconstructed. The adder 155 adds the reconstructed residual signal to aprediction signal output from the inter predictor 221 or the intrapredictor 222, so that a reconstructed signal (reconstructed picture,reconstructed block, reconstructed sample array) may be generated. Whenthere is no residual for a processing target block as in a case wherethe skip mode is applied, the predicted block may be used as areconstructed block. The adder 250 may be called a reconstructor or areconstructed block generator. The generated reconstructed signal may beused for intra prediction of a next processing target block in thecurrent block, and as described later, may be used for inter predictionof a next picture through filtering.

Meanwhile, in the picture encoding and/or reconstructing process, lumamapping with chroma scaling (LMCS) may be applied.

The filter 260 may improve subjective/objective video quality byapplying the filtering to the reconstructed signal. For example, thefilter 260 may generate a modified reconstructed picture by applyingvarious filtering methods to the reconstructed picture, and may storethe modified reconstructed picture in the memory 270, specifically inthe DPB of the memory 270.

The various filtering methods may include, for example, deblockingfiltering, sample adaptive offset, an adaptive loop filter, a bilateralfilter or the like. As discussed later in the description of eachfiltering method, the filter 260 may generate various informationrelating to filtering, and transmit the generated information to theentropy encoder 240. The information on the filtering may be encoded inthe entropy encoder 240 and output in the form of a bitstream.

The modified reconstructed picture which has been transmitted to thememory 270 may be used as a reference picture in the inter predictor221. Through this, the encoding apparatus can avoid prediction mismatchin the encoding apparatus 100 and a decoding apparatus when the interprediction is applied, and can also improve coding efficiency.

The memory 270 DPB may store the modified reconstructed picture in orderto use it as a reference picture in the inter predictor 221. The memory270 may store motion information of a block in the current picture, fromwhich motion information has been derived (or encoded) and/or motioninformation of blocks in an already reconstructed picture. The storedmotion information may be transmitted to the inter predictor 221 to beutilized as motion information of a neighboring block or motioninformation of a temporal neighboring block. The memory 270 may storereconstructed samples of reconstructed blocks in the current picture,and transmit them to the intra predictor 222.

FIG. 3 is a diagram schematically illustrating a configuration of avideo/image decoding apparatus to which the present disclosure isapplicable.

Referring to FIG. 3 , the video decoding apparatus 300 may include anentropy decoder 310, a residual processor 320, a predictor 330, an adder340, a filter 350 and a memory 360. The predictor 330 may include aninter predictor 331 and an intra predictor 332. The residual processor320 may include a dequantizer 321 and an inverse transformer 321. Theentropy decoder 310, the residual processor 320, the predictor 330, theadder 340, and the filter 350, which have been described above, may beconstituted by one or more hardware components (e.g., decoder chipsetsor processors) according to an embodiment. Further, the memory 360 mayinclude a decoded picture buffer (DPB), and may be constituted by adigital storage medium. The hardware component may further include thememory 360 as an internal/external component.

When a bitstream including video/image information is input, thedecoding apparatus 300 may reconstruct an image correspondingly to aprocess by which video/image information has been processed in theencoding apparatus of FIG. 2 . For example, the decoding apparatus 300may derive units/blocks based on information relating to block partitionobtained from the bitstream. The decoding apparatus 300 may performdecoding by using a processing unit applied in the encoding apparatus.Therefore, the processing unit of decoding may be, for example, a codingunit, which may be partitioned along the quad-tree structure, thebinary-tree structure, and/or the ternary-tree structure from a codingtree unit or a largest coding unit. One or more transform units may bederived from the coding unit. And, the reconstructed image signaldecoded and output through the decoding apparatus 300 may be reproducedthrough a reproducer.

The decoding apparatus 300 may receive a signal output from the encodingapparatus of FIG. 2 in the form of a bitstream, and the received signalmay be decoded through the entropy decoder 310. For example, the entropydecoder 310 may parse the bitstream to derive information (e.g.,video/image information) required for image reconstruction (or picturereconstruction). The video/image information may further includeinformation on various parameter sets such as an adaptation parameterset (APS), a picture parameter set (PPS), a sequence parameter set(SPS), a video parameter set (VPS) or the like. Further, the video/imageinformation may further include general constraint information. Thedecoding apparatus may decode a picture further based on information onthe parameter set and/or the general constraint information. In thepresent disclosure, signaled/received information and/or syntaxelements, which will be described later, may be decoded through thedecoding procedure and be obtained from the bitstream. For example, theentropy decoder 310 may decode information in the bitstream based on acoding method such as exponential Golomb encoding, CAVLC, CABAC, or thelike, and may output a value of a syntax element necessary for imagereconstruction and quantized values of a transform coefficient regardinga residual. More specifically, a CABAC entropy decoding method mayreceive a bin corresponding to each syntax element in a bitstream,determine a context model using decoding target syntax elementinformation and decoding information of neighboring and decoding targetblocks, or information of symbol/bin decoded in a previous step, predictbin generation probability according to the determined context model andperform arithmetic decoding of the bin to generate a symbolcorresponding to each syntax element value. Here, the CABAC entropydecoding method may update the context model using information of asymbol/bin decoded for a context model of the next symbol/bin afterdetermination of the context model. Information on prediction amonginformation decoded in the entropy decoder 310 may be provided to thepredictor (inter predictor 332 and intra predictor 331), and residualvalues, that is, quantized transform coefficients, on which entropydecoding has been performed in the entropy decoder 310, and associatedparameter information may be input to the residual processor 320. Theresidual processor 320 may derive a residual signal (residual block,residual samples, residual sample array). Further, information onfiltering among information decoded in the entropy decoder 310 may beprovided to the filter 350. Meanwhile, a receiver (not shown) whichreceives a signal output from the encoding apparatus may furtherconstitute the decoding apparatus 300 as an internal/external element,and the receiver may be a component of the entropy decoder 310.Meanwhile, the decoding apparatus according to the present disclosuremay be called a video/image/picture coding apparatus, and the decodingapparatus may be classified into an information decoder(video/image/picture information decoder) and a sample decoder(video/image/picture sample decoder). The information decoder mayinclude the entropy decoder 310, and the sample decoder may include atleast one of the dequantizer 321, the inverse transformer 322, the adder340, the filter 350, the memory 360, the inter predictor 332, and theintra predictor 331.

The dequantizer 321 may output transform coefficients by dequantizingthe quantized transform coefficients. The dequantizer 321 may rearrangethe quantized transform coefficients in the form of a two-dimensionalblock. In this case, the rearrangement may perform rearrangement basedon an order of coefficient scanning which has been performed in theencoding apparatus. The dequantizer 321 may perform dequantization onthe quantized transform coefficients using quantization parameter (e.g.,quantization step size information), and obtain transform coefficients.

The deqauntizer 322 obtains a residual signal (residual block, residualsample array) by inverse transforming transform coefficients.

The predictor may perform prediction on the current block, and generatea predicted block including prediction samples for the current block.The predictor may determine whether intra prediction or inter predictionis applied to the current block based on the information on predictionoutput from the entropy decoder 310, and specifically may determine anintra/inter prediction mode.

The predictor may generate a prediction signal based on variousprediction methods. For example, the predictor may apply intraprediction or inter prediction for prediction on one block, and, aswell, may apply intra prediction and inter prediction at the same time.This may be called combined inter and intra prediction (CIIP). Inaddition, the predictor may perform intra block copy (IBC) forprediction on a block. The intra block copy may be used for contentimage/video coding of a game or the like, such as screen content coding(SCC). Although the IBC basically performs prediction in a currentblock, it can be performed similarly to inter prediction in that itderives a reference block in a current block. That is, the IBC may useat least one of inter prediction techniques described in the presentdisclosure.

The intra predictor 331 may predict the current block by referring tothe samples in the current picture. The referred samples may be locatedin the neighbor of or apart from the current block according to theprediction mode. In the intra prediction, prediction modes may include aplurality of non-directional modes and a plurality of directional modes.The intra predictor 331 may determine the prediction mode applied to thecurrent block by using the prediction mode applied to the neighboringblock.

The inter predictor 332 may derive a predicted block for the currentblock based on a reference block (reference sample array) specified by amotion vector on a reference picture. At this time, in order to reducethe amount of motion information transmitted in the inter predictionmode, the motion information may be predicted on a block, subblock, orsample basis based on correlation of motion information between theneighboring block and the current block. The motion information mayinclude a motion vector and a reference picture index. The motioninformation may further include inter prediction direction (L0prediction, L1 prediction, Bi prediction, etc.) information. In the caseof inter prediction, the neighboring block may include a spatialneighboring block existing in the current picture and a temporalneighboring block existing in the reference picture. For example, theinter predictor 332 may configure a motion information candidate listbased on neighboring blocks, and derive a motion vector and/or areference picture index of the current block based on received candidateselection information. Inter prediction may be performed based onvarious prediction modes, and the information on prediction may includeinformation indicating a mode of inter prediction for the current block.

The adder 340 may generate a reconstructed signal (reconstructedpicture, reconstructed block, reconstructed sample array) by adding theobtained residual signal to the prediction signal (predicted block,prediction sample array) output from the predictor 330. When there is noresidual for a processing target block as in a case where the skip modeis applied, the predicted block may be used as a reconstructed block.

The adder 340 may be called a reconstructor or a reconstructed blockgenerator. The generated reconstructed signal may be used for intraprediction of a next processing target block in the current block, andas described later, may be output through filtering or be used for interprediction of a next picture.

Meanwhile, in the picture decoding process, luma mapping with chromascaling (LMCS) may be applied.

The filter 350 may improve subjective/objective video quality byapplying the filtering to the reconstructed signal. For example, thefilter 350 may generate a modified reconstructed picture by applyingvarious filtering methods to the reconstructed picture, and may transmitthe modified reconstructed picture in the memory 360, specifically inthe DPB of the memory 360. The various filtering methods may include,for example, deblocking filtering, sample adaptive offset, an adaptiveloop filter, a bilateral filter or the like.

The (modified) reconstructed picture which has been stored in the DPB ofthe memory 360 may be used as a reference picture in the inter predictor332. The memory 360 may store motion information of a block in thecurrent picture, from which motion information has been derived (ordecoded) and/or motion information of blocks in an already reconstructedpicture. The stored motion information may be transmitted to the interpredictor 260 to be utilized as motion information of a neighboringblock or motion information of a temporal neighboring block. The memory360 may store reconstructed samples of reconstructed blocks in thecurrent picture, and transmit them to the intra predictor 331.

In this specification, the examples described in the predictor 330, thedequantizer 321, the inverse transformer 322, and the filter 350 of thedecoding apparatus 300 may be similarly or correspondingly applied tothe predictor 220, the dequantizer 234, the inverse transformer 235, andthe filter 260 of the encoding apparatus 200, respectively.

As described above, prediction is performed in order to increasecompression efficiency in performing video coding. Through this, apredicted block including prediction samples for a current block, whichis a coding target block, may be generated. Here, the predicted blockincludes prediction samples in a space domain (or pixel domain). Thepredicted block may be indentically derived in the encoding apparatusand the decoding apparatus, and the encoding apparatus may increaseimage coding efficiency by signaling to the decoding apparatus notoriginal sample value of an original block itself but information onresidual (residual information) between the original block and thepredicted block. The decoding apparatus may derive a residual blockincluding residual samples based on the residual information, generate areconstructed block including reconstructed samples by adding theresidual block to the predicted block, and generate a reconstructedpicture including reconstructed blocks.

The residual information may be generated through transform andquantization procedures. For example, the encoding apparatus may derivea residual block between the original block and the predicted block,derive transform coefficients by performing a transform procedure onresidual samples (residual sample array) included in the residual block,and derive quantized transform coefficients by performing a quantizationprocedure on the transform coefficients, so that it may signalassociated residual information to the decoding apparatus (through abitstream). Here, the residual information may include valueinformation, position information, a transform technique, transformkernel, a quantization parameter or the like of the quantized transformcoefficients. The decoding apparatus may perform aquantization/dequantization procedure and derive the residual samples(or residual sample block), based on residual information. The decodingapparatus may generate a reconstructed block based on a predicted blockand the residual block. The encoding apparatus may derive a residualblock by dequantizing/inverse transforming quantized transformcoefficients for reference for inter prediction of a next picture, andmay generate a reconstructed picture based on this.

FIG. 4 schematically illustrates a multiple transform techniqueaccording to an embodiment of the present disclosure.

Referring to FIG. 4 , a transformer may correspond to the transformer inthe encoding apparatus of foregoing FIG. 2 , and an inverse transformermay correspond to the inverse transformer in the encoding apparatus offoregoing FIG. 2 , or to the inverse transformer in the decodingapparatus of FIG. 3 .

The transformer may derive (primary) transform coefficients byperforming a primary transform based on residual samples (residualsample array) in a residual block (S410). This primary transform may bereferred to as a core transform. Herein, the primary transform may bebased on multiple transform selection (MTS), and when a multipletransform is applied as the primary transform, it may be referred to asa multiple core transform.

The multiple core transform may represent a method of transformingadditionally using discrete cosine transform (DCT) type 2 and discretesine transform (DST) type 7, DCT type 8, and/or DST type 1. That is, themultiple core transform may represent a transform method of transforminga residual signal (or residual block) of a space domain into transformcoefficients (or primary transform coefficients) of a frequency domainbased on a plurality of transform kernels selected from among the DCTtype 2, the DST type 7, the DCT type 8 and the DST type 1. Herein, theprimary transform coefficients may be called temporary transformcoefficients from the viewpoint of the transformer.

In other words, when the conventional transform method is applied,transform coefficients might be generated by applying transform from aspace domain to a frequency domain for a residual signal (or residualblock) based on the DCT type 2. Unlike to this, when the multiple coretransform is applied, transform coefficients (or primary transformcoefficients) may be generated by applying transform from a space domainto a frequency domain for a residual signal (or residual block) based onthe DCT type 2, the DST type 7, the DCT type 8, and/or DST type 1.Herein, the DCT type 2, the DST type 7, the DCT type 8, and the DST type1 may be called a transform type, transform kernel or transform core.These DCT/DST transform types can be defined based on basis functions.

When the multiple core transform is performed, a vertical transformkernel and a horizontal transform kernel for a target block may beselected from among the transform kernels, a vertical transform may beperformed on the target block based on the vertical transform kernel,and a horizontal transform may be performed on the target block based onthe horizontal transform kernel. Here, the horizontal transform mayindicate a transform on horizontal components of the target block, andthe vertical transform may indicate a transform on vertical componentsof the target block. The vertical transform kernel/horizontal transformkernel may be adaptively determined based on a prediction mode and/or atransform index for the target block (CU or subblock) including aresidual block.

Further, according to an example, if the primary transform is performedby applying the MTS, a mapping relationship for transform kernels may beset by setting specific basis functions to predetermined values andcombining basis functions to be applied in the vertical transform or thehorizontal transform. For example, when the horizontal transform kernelis expressed as trTypeHor and the vertical direction transform kernel isexpressed as trTypeVer, a trTypeHor or trTypeVer value of 0 may be setto DCT2, a trTypeHor or trTypeVer value of 1 may be set to DST7, and atrTypeHor or trTypeVer value of 2 may be set to DCT8.

In this case, MTS index information may be encoded and signaled to thedecoding apparatus to indicate any one of a plurality of transformkernel sets. For example, an MTS index of 0 may indicate that bothtrTypeHor and trTypeVer values are 0, an MTS index of 1 may indicatethat both trTypeHor and trTypeVer values are 1, an MTS index of 2 mayindicate that the trTypeHor value is 2 and the trTypeVer value. Is 1, anMTS index of 3 may indicate that the trTypeHor value is 1 and thetrTypeVer value is 2, and an MTS index of 4 may indicate that both bothtrTypeHor and trTypeVer values are 2.

In one example, transform kernel sets according to MTS index informationare illustrated in the following table.

TABLE 1 tu_ 

 ts_idx[ x0 ][ y0 ] 0 1 2 3 4  

 TypeHor 0 1 2 1 2  

  0 1 1 2 2

indicates data missing or illegible when filed

The transformer may derive modified (secondary) transform coefficientsby performing the secondary transform based on the (primary) transformcoefficients (S420). The primary transform is a transform from a spatialdomain to a frequency domain, and the secondary transform refers totransforming into a more compressive expression by using a correlationexisting between (primary) transform coefficients. The secondarytransform may include a non-separable transform. In this case, thesecondary transform may be called a non-separable secondary transform(NSST), or a mode-dependent non-separable secondary transform (MDNSST).The non-separable secondary transform may represent a transform whichgenerates modified transform coefficients (or secondary transformcoefficients) for a residual signal by secondary-transforming, based ona non-separable transform matrix, (primary) transform coefficientsderived through the primary transform. At this time, the verticaltransform and the horizontal transform may not be applied separately (orhorizontal and vertical transforms may not be applied independently) tothe (primary) transform coefficients, but the transforms may be appliedat once based on the non-separable transform matrix. In other words, thenon-separable secondary transform may represent a transform method inwhich the vertical and horizontal components of the (primary) transformcoefficients are not separated, and for example, two-dimensional signals(transform coefficients) are re-arranged to a one-dimensional signalthrough a certain determined direction (e.g., row-first direction orcolumn-first direction), and then modified transform coefficients (orsecondary transform coefficients) are generated based on thenon-separable transform matrix. For example, according to a row-firstorder, M×N blocks are disposed in a line in an order of a first row, asecond row, . . . , and an Nth row. According to a column-first order,M×N blocks are disposed in a line in an order of a first column, asecond column, . . . , and an Nth column. The non-separable secondarytransform may be applied to a top-left region of a block configured with(primary) transform coefficients (hereinafter, may be referred to as atransform coefficient block). For example, if the width (W) and theheight (H) of the transform coefficient block are all equal to orgreater than 8, an 8×8 non-separable secondary transform may be appliedto a top-left 8×8 region of the transform coefficient block. Further, ifthe width (W) and the height (H) of the transform coefficient block areall equal to or greater than 4, and the width (W) or the height (H) ofthe transform coefficient block is less than 8, then a 4×4 non-separablesecondary transform may be applied to a top-left min(8,W)×min(8,H)region of the transform coefficient block. However, the embodiment isnot limited to this, and for example, even if only the condition thatthe width (W) or height (H) of the transform coefficient block is equalto or greater than 4 is satisfied, the 4×4 non-separable secondarytransform may be applied to the top-left min(8,W)×min(8,H) region of thetransform coefficient block.

Specifically, for example, if a 4×4 input block is used, thenon-separable secondary transform may be performed as follows.

The 4×4 input block X may be represented as follows.

$\begin{matrix}{X = \begin{bmatrix}X_{00} & X_{01} & X_{02} & X_{03} \\X_{10} & X_{11} & X_{12} & X_{13} \\X_{20} & X_{21} & X_{22} & X_{23} \\X_{30} & X_{31} & X_{32} & X_{33}\end{bmatrix}} & \left\lbrack {{Equation}1} \right\rbrack\end{matrix}$

If the X is represented in the form of a vector, the vector

may be represented as below.

=[X ₀₀ X ₀₁ X ₀₂ X ₀₃ X ₁₀ X ₁₁ X ₁₂ X ₁₃ X ₂₀ X ₂₁ X ₂₂ X ₂₃ X ₃₀ X ₃₁X ₃₂ X ₃₃]^(T)   [Equation 2]

In Equation 2, the vector

is a one-dimensional vector obtained by rearranging the two-dimensionalblock X of Equation 1 according to the row-first order.

In this case, the secondary non-separable transform may be calculated asbelow.

=T·

  [Equation 3]

In this equation,

represents a transform coefficient vector, and T represents a 16×16(non-separable) transform matrix.

Through foregoing Equation 3, a 16×1 transform coefficient vector

may be derived, and the

may be re-organized into a 4×4 block through a scan order (horizontal,vertical, diagonal and the like). However, the above-describedcalculation is an example, and hypercube-Givens transform (HyGT) or thelike may be used for the calculation of the non-separable secondarytransform in order to reduce the computational complexity of thenon-separable secondary transform.

Meanwhile, in the non-separable secondary transform, a transform kernel(or transform core, transform type) may be selected to be modedependent. In this case, the mode may include the intra prediction modeand/or the inter prediction mode.

As described above, the non-separable secondary transform may beperformed based on an 8×8 transform or a 4×4 transform determined basedon the width (W) and the height (H) of the transform coefficient block.The 8×8 transform refers to a transform that is applicable to an 8×8region included in the transform coefficient block when both W and H areequal to or greater than 8, and the 8×8 region may be a top-left 8×8region in the transform coefficient block. Similarly, the 4×4 transformrefers to a transform that is applicable to a 4×4 region included in thetransform coefficient block when both W and H are equal to or greaterthan 4, and the 4×4 region may be a top-left 4×4 region in the transformcoefficient block. . For example, an 8×8 transform kernel matrix may bea 64×64/16×64 matrix, and a 4×4 transform kernel matrix may be a16×16/8×16 matrix.

Here, to select a mode-dependent transform kernel, two non-separablesecondary transform kernels per transform set for a non-separablesecondary transform may be configured for both the 8×8 transform and the4×4 transform, and there may be four transform sets. That is, fourtransform sets may be configured for the 8×8 transform, and fourtransform sets may be configured for the 4×4 transform. In this case,each of the four transform sets for the 8×8 transform may include two8×8 transform kernels, and each of the four transform sets for the 4×4transform may include two 4×4 transform kernels.

However, as the size of the transform, that is, the size of a region towhich the transform is applied, may be, for example, a size other than8×8 or 4×4, the number of sets may be n, and the number of transformkernels in each set may be k.

The transform set may be referred to as an NSST set or an LFNST set. Aspecific set among the transform sets may be selected, for example,based on the intra prediction mode of the current block (CU orsubblock). A low-frequency non-separable transform (LFNST) may be anexample of a reduced non-separable transform, which will be describedlater, and represents a non-separable transform for a low frequencycomponent.

For reference, for example, the intra prediction mode may include twonon-directinoal (or non-angular) intra prediction modes and 65directional (or angular) intra prediction modes. The non-directionalintra prediction modes may include a planar intra prediction mode of No.0 and a DC intra prediction mode of No. 1, and the directional intraprediction modes may include 65 intra prediction modes of Nos. 2 to 66.However, this is an example, and this document may be applied even whenthe number of intra prediction modes is different. Meanwhile, in somecases, intra prediction mode No. 67 may be further used, and the intraprediction mode No. 67 may represent a linear model (LM) mode.

FIG. 5 exemplarily shows intra directional modes of 65 predictiondirections.

Referring to FIG. 5 , on the basis of intra prediction mode 34 having aleft upward diagonal prediction direction, the intra prediction modesmay be divided into intra prediction modes having horizontaldirectionality and intra prediction modes having verticaldirectionality. In FIG. 5 , H and V denote horizontal directionality andvertical directionality, respectively, and numerals −32 to 32 indicatedisplacements in 1/32 units on a sample grid position. These numeralsmay represent an offset for a mode index value. Intra prediction modes 2to 33 have the horizontal directionality, and intra prediction modes 34to 66 have the vertical directionality. Strictly speaking, intraprediction mode 34 may be considered as being neither horizontal norvertical, but may be classified as belonging to the horizontaldirectionality in determining a transform set of a secondary transform.This is because input data is transposed to be used for a verticaldirection mode symmetrical on the basis of intra prediction mode 34, andan input data alignment method for a horizontal mode is used for intraprediction mode 34. Transposing input data means that rows and columnsof two-dimensional M×N block data are switched into N×M data. Intraprediction mode 18 and intra prediction mode 50 may represent ahorizontal intra prediction mode and a vertical intra prediction mode,respectively, and intra prediction mode 2 may be referred to as a rightupward diagonal intra prediction mode because intra prediction mode 2has a left reference pixel and performs prediction in a right upwarddirection. Likewise, intra prediction mode 34 may be referred to as aright downward diagonal intra prediction mode, and intra prediction mode66 may be referred to as a left downward diagonal intra prediction mode.

According to an example, the four transform sets according to the intraprediction mode may be mapped, for example, as shown in the followingtable.

TABLE 2 lfnstPredModeIntra lfnstTrSetIdx lfnstPredModeIntra < 0 1 0 <=lfnstPredModeIntra <= 1 0  2 <= lfnstPredModeIntra <= 12 1 13 <=lfnstPredModeIntra <= 23 2 24 <= lfnstPredModeIntra <= 44 3 45 <=lfnstPredModeIntra <= 55 2 56 <= lfnstPredModeIntra <= 80 1 81 <=lfnstPredModeIntra <= 83 0

As shown in Table 2, any one of the four transform sets, that is,lfnstTrSetIdx, may be mapped to any one of four indexes, that is, 0 to3, according to the intra prediction mode.

When it is determined that a specific set is used for the non-separabletransform, one of k transform kernels in the specific set may beselected through a non-separable secondary transform index. An encodingapparatus may derive a non-separable secondary transform indexindicating a specific transform kernel based on a rate-distortion (RD)check and may signal the non-separable secondary transform index to adecoding apparatus. The decoding apparatus may select one of the ktransform kernels in the specific set based on the non-separablesecondary transform index. For example, lfnst index value 0 may refer toa first non-separable secondary transform kernel, lfnst index value 1may refer to a second non-separable secondary transform kernel, andlfnst index value 2 may refer to a third non-separable secondarytransform kernel. Alternatively, lfnst index value 0 may indicate thatthe first non-separable secondary transform is not applied to the targetblock, and lfnst index values 1 to 3 may indicate the three transformkernels.

The transformer may perform the non-separable secondary transform basedon the selected transform kernels, and may obtain modified (secondary)transform coefficients. As described above, the modified transformcoefficients may be derived as transform coefficients quantized throughthe quantizer, and may be encoded and signaled to the decoding apparatusand transferred to the dequantizer/inverse transformer in the encodingapparatus.

Meanwhile, as described above, if the secondary transform is omitted,(primary) transform coefficients, which are an output of the primary(separable) transform, may be derived as transform coefficientsquantized through the quantizer as described above, and may be encodedand signaled to the decoding apparatus and transferred to thedequantizer/inverse transformer in the encoding apparatus.

The inverse transformer may perform a series of procedures in theinverse order to that in which they have been performed in theabove-described transformer. The inverse transformer may receive(dequantized) transformer coefficients, and derive (primary) transformcoefficients by performing a secondary (inverse) transform (S450), andmay obtain a residual block (residual samples) by performing a primary(inverse) transform on the (primary) transform coefficients (S460). Inthis connection, the primary transform coefficients may be calledmodified transform coefficients from the viewpoint of the inversetransformer. As described above, the encoding apparatus and the decodingapparatus may generate the reconstructed block based on the residualblock and the predicted block, and may generate the reconstructedpicture based on the reconstructed block.

The decoding apparatus may further include a secondary inverse transformapplication determinator (or an element to determine whether to apply asecondary inverse transform) and a secondary inverse transformdeterminator (or an element to determine a secondary inverse transform).The secondary inverse transform application determinator may determinewhether to apply a secondary inverse transform. For example, thesecondary inverse transform may be an NSST, an RST, or an LFNST and thesecondary inverse transform application determinator may determinewhether to apply the secondary inverse transform based on a secondarytransform flag obtained by parsing the bitstream. In another example,the secondary inverse transform application determinator may determinewhether to apply the secondary inverse transform based on a transformcoefficient of a residual block.

The secondary inverse transform determinator may determine a secondaryinverse transform. In this case, the secondary inverse transformdeterminator may determine the secondary inverse transform applied tothe current block based on an LFNST (NSST or RST) transform setspecified according to an intra prediction mode. In an embodiment, asecondary transform determination method may be determined depending ona primary transform determination method. Various combinations ofprimary transforms and secondary transforms may be determined accordingto the intra prediction mode. Further, in an example, the secondaryinverse transform determinator may determine a region to which asecondary inverse transform is applied based on the size of the currentblock.

Meanwhile, as described above, if the secondary (inverse) transform isomitted, (dequantized) transform coefficients may be received, theprimary (separable) inverse transform may be performed, and the residualblock (residual samples) may be obtained. As described above, theencoding apparatus and the decoding apparatus may generate thereconstructed block based on the residual block and the predicted block,and may generate the reconstructed picture based on the reconstructedblock.

Meanwhile, in the present disclosure, a reduced secondary transform(RST) in which the size of a transform matrix (kernel) is reduced may beapplied in the concept of NSST in order to reduce the amount ofcomputation and memory required for the non-separable secondarytransform.

Meanwhile, the transform kernel, the transform matrix, and thecoefficient constituting the transform kernel matrix, that is, thekernel coefficient or the matrix coefficient, described in the presentdisclosure may be expressed in 8 bits. This may be a condition forimplementation in the decoding apparatus and the encoding apparatus, andmay reduce the amount of memory required to store the transform kernelwith a performance degradation that can be reasonably accommodatedcompared to the existing 9 bits or 10 bits. In addition, the expressingof the kernel matrix in 8 bits may allow a small multiplier to be used,and may be more suitable for single instruction multiple data (SIMD)instructions used for optimal software implementation.

In the present specification, the term “RST” may mean a transform whichis performed on residual samples for a target block based on a transformmatrix whose size is reduced according to a reduced factor. In the caseof performing the reduced transform, the amount of computation requiredfor transform may be reduced due to a reduction in the size of thetransform matrix. That is, the RST may be used to address thecomputational complexity issue occurring at the non-separable transformor the transform of a block of a great size.

RST may be referred to as various terms, such as reduced transform,reduced secondary transform, reduction transform, simplified transform,simple transform, and the like, and the name which RST may be referredto as is not limited to the listed examples. Alternatively, since theRST is mainly performed in a low frequency region including a non-zerocoefficient in a transform block, it may be referred to as aLow-Frequency Non-Separable Transform (LFNST). The transform index maybe referred to as an LFNST index.

Meanwhile, when the secondary inverse transform is performed based onRST, the inverse transformer 235 of the encoding apparatus 200 and theinverse transformer 322 of the decoding apparatus 300 may include aninverse reduced secondary transformer which derives modified transformcoefficients based on the inverse RST of the transform coefficients, andan inverse primary transformer which derives residual samples for thetarget block based on the inverse primary transform of the modifiedtransform coefficients. The inverse primary transform refers to theinverse transform of the primary transform applied to the residual. Inthe present disclosure, deriving a transform coefficient based on atransform may refer to deriving a transform coefficient by applying thetransform.

FIG. 6 is a diagram illustrating an RST according to an embodiment ofthe present disclosure.

In the present disclosure, a “target block” may refer to a current blockto be coded, a residual block, or a transform block.

In the RST according to an example, an N-dimensional vector may bemapped to an R-dimensional vector located in another space, so that thereduced transform matrix may be determined, where R is less than N. Nmay mean the square of the length of a side of a block to which thetransform is applied, or the total number of transform coefficientscorresponding to a block to which the transform is applied, and thereduced factor may mean an R/N value. The reduced factor may be referredto as a reduced factor, reduction factor, simplified factor, simplefactor or other various terms. Meanwhile, R may be referred to as areduced coefficient, but according to circumstances, the reduced factormay mean R. Further, according to circumstances, the reduced factor maymean the N/R value.

In an example, the reduced factor or the reduced coefficient may besignaled through a bitstream, but the example is not limited to this.For example, a predefined value for the reduced factor or the reducedcoefficient may be stored in each of the encoding apparatus 200 and thedecoding apparatus 300, and in this case, the reduced factor or thereduced coefficient may not be signaled separately.

The size of the reduced transform matrix according to an example may beR×N less than N×N, the size of a conventional transform matrix, and maybe defined as in Equation 4 below.

$\begin{matrix}{T_{RxN} = \begin{bmatrix}t_{11} & t_{12} & t_{13} & \ldots & t_{1N} \\t_{21} & t_{22} & t_{23} & & t_{2N} \\ & \vdots & & \ddots & \vdots \\t_{R1} & t_{R2} & t_{R3} & \ldots & t_{RN}\end{bmatrix}} & \left\lbrack {{Equation}4} \right\rbrack\end{matrix}$

The matrix Tin the Reduced Transform block shown in FIG. 6(a) may meanthe matrix _(R×N) of Equation 4. As shown in FIG. 6(a), when the reducedtransform matrix T_(R×N) is multiplied to residual samples for thetarget block, transform coefficients for the target block may bederived.

In an example, if the size of the block to which the transform isapplied is 8×8 and R=16 (i.e., R/N=16/64=1/4), then the RST according toFIG. 6(a) may be expressed as a matrix operation as shown in Equation 5below. In this case, memory and multiplication calculation can bereduced to approximately ¼ by the reduced factor.

In the present disclosure, a matrix operation may be understood as anoperation of multiplying a column vector by a matrix, disposed on theleft of the column vector, to obtain a column vector.

$\begin{matrix}{\begin{bmatrix}t_{1,1} & t_{1,2} & t_{1,3} & \ldots & t_{1,64} \\t_{2,1} & t_{2,2} & t_{2,3} & & t_{2,64} \\ & \vdots & & \ddots & \vdots \\t_{16,1} & t_{16,2} & t_{16,3} & \ldots & t_{16,64}\end{bmatrix} \times \begin{bmatrix}r_{1} \\r_{2} \\ \vdots \\r_{64}\end{bmatrix}} & \left\lbrack {{Equation}5} \right\rbrack\end{matrix}$

In Equation 5, r₁ to r₆₄ may represent residual samples for the targetblock and may be specifically transform coefficients generated byapplying a primary transform. As a result of the calculation of Equation5 transform coefficients c₁ for the target block may be derived, and aprocess of deriving c₁ may be as in Equation 6.

$\begin{matrix}\begin{matrix}\begin{matrix}{{for}i{from}{to}{}{R:}} \\{c_{i} = 0} \\{{for}j{from}1{to}N} \\{c_{i}+={t_{i.j}*r_{j}}}\end{matrix}\end{matrix} & \left\lbrack {{Equation}6} \right\rbrack\end{matrix}$

As a result of the calculation of Equation 6, transform coefficients c₁to c_(R) for the target block may be derived. That is, when R=16,transform coefficients c₁ to c₁₆ for the target block may be derived.If, instead of RST, a regular transform is applied and a transformmatrix of 64×64 (N×N) size is multiplied to residual samples of 64×1(N×1) size, then only 16 (R) transform coefficients are derived for thetarget block because RST was applied, although 64 (N) transformcoefficients are derived for the target block. Since the total number oftransform coefficients for the target block is reduced from N to R, theamount of data transmitted by the encoding apparatus 200 to the decodingapparatus 300 decreases, so efficiency of transmission between theencoding apparatus 200 and the decoding apparatus 300 can be improved.

When considered from the viewpoint of the size of the transform matrix,the size of the regular transform matrix is 64×64 (N×N), but the size ofthe reduced transform matrix is reduced to 16×64 (R×N), so memory usagein a case of performing the RST can be reduced by an R/N ratio whencompared with a case of performing the regular transform. In addition,when compared to the number of multiplication calculations N×N in a caseof using the regular transform matrix, the use of the reduced transformmatrix can reduce the number of multiplication calculations by the R/Nratio (R×N).

In an example, the transformer 232 of the encoding apparatus 200 mayderive transform coefficients for the target block by performing theprimary transform and the RST-based secondary transform on residualsamples for the target block. These transform coefficients may betransferred to the inverse transformer of the decoding apparatus 300,and the inverse transformer 322 of the decoding apparatus 300 may derivethe modified transform coefficients based on the inverse reducedsecondary transform (RST) for the transform coefficients, and may deriveresidual samples for the target block based on the inverse primarytransform for the modified transform coefficients.

The size of the inverse RST matrix T_(N×R) according to an example isN×R less than the size N×N of the regular inverse transform matrix, andis in a transpose relationship with the reduced transform matrix T_(R×N)shown in Equation 4.

The matrix V in the Reduced Inv. Transform block shown in FIG. 6(b) maymean the inverse RST matrix T_(R×N) ^(T) (the superscript T meanstranspose). When the inverse RST matrix T_(R×N) ^(T) is multiplied tothe transform coefficients for the target block as shown in FIG. 6(b),the modified transform coefficients for the target block or the residualsamples for the current block may be derived. The inverse RST matrixT_(R×N) ^(T) may be expressed as (T_(R×N) ^(T))_(N×R).

More specifically, when the inverse RST is applied as the secondaryinverse transform, the modified transform coefficients for the targetblock may be derived when the inverse RST matrix T_(R×N) ^(T) ismultiplied to the transform coefficients for the target block.Meanwhile, the inverse RST may be applied as the inverse primarytransform, and in this case, the residual samples for the target blockmay be derived when the inverse RST matrix T_(R×N) ^(T) is multiplied tothe transform coefficients for the target block.

In an example, if the size of the block to which the inverse transformis applied is 8×8 and R=16 (i.e., R/N=16/64=1/4), then the RST accordingto FIG. 6(b) may be expressed as a matrix operation as shown in Equation7 below.

$\begin{matrix}{\begin{bmatrix}t_{1,1} & & t_{2,1} & & t_{16,1} \\t_{1,2} & & t_{2,2} & {\ldots} & t_{16,2} \\t_{1,3} & & t_{2,3} & & t_{16,3} \\ \vdots & & \vdots & & \vdots \\ & \vdots & & \ddots & \vdots \\t_{1,64} & & t_{2,64} & \ldots & t_{16,64}\end{bmatrix} \times \begin{bmatrix}c_{1} \\c_{2} \\ \vdots \\c_{16}\end{bmatrix}} & \left\lbrack {{Equation}7} \right\rbrack\end{matrix}$

In Equation 7, c₁ to c₁₆ may represent the transform coefficients forthe target block. As a result of the calculation of Equation 7, r_(i)representing the modified transform coefficients for the target block orthe residual samples for the target block may be derived, and theprocess of deriving r_(i) may be as in Equation 8.

$\begin{matrix}{{{For}i{from}1{to}N}{r = 0}{{for}j{from}1{to}R}{r-={t_{j}*c_{j}}}} & \left\lbrack {{Equation}8} \right\rbrack\end{matrix}$

As a result of the calculation of Equation 8, r₁ to r_(N) representingthe modified transform coefficients for the target block or the residualsamples for the target block may be derived. When considered from theviewpoint of the size of the inverse transform matrix, the size of theregular inverse transform matrix is 64×64 (N×N), but the size of thereduced inverse transform matrix is reduced to 64×16 (R×N), so memoryusage in a case of performing the inverse RST can be reduced by an R/Nratio when compared with a case of performing the regular inversetransform. In addition, when compared to the number of multiplicationcalculations N×N in a case of using the regular inverse transformmatrix, the use of the reduced inverse transform matrix can reduce thenumber of multiplication calculations by the R/N ratio (N×R).

A transform set configuration shown in Table 2 may also be applied to an8×8 RST. That is, the 8×8 RST may be applied according to a transformset in Table 2. Since one transform set includes two or three transforms(kernels) according to an intra prediction mode, it may be configured toselect one of up to four transforms including that in a case where nosecondary transform is applied. In a transform where no secondarytransform is applied, it may be considered to apply an identity matrix.Assuming that indexes 0, 1, 2, and 3 are respectively assigned to thefour transforms (e.g., index 0 may be allocated to a case where anidentity matrix is applied, that is, a case where no secondary transformis applied), a transform index or an lfnst index as a syntax element maybe signaled for each transform coefficient block, thereby designating atransform to be applied. That is, for a top-left 8×8 block, through thetransform index, it is possible to designate an 8×8 RST in an RSTconfiguration, or to designate an 8×8 lfnst when the LFNST is applied.The 8×8 lfnst and the 8×8 RST refer to transforms applicable to an 8×8region included in the transform coefficient block when both W and H ofthe target block to be transformed are equal to or greater than 8, andthe 8×8 region may be a top-left 8×8 region in the transform coefficientblock. Similarly, a 4×4 lfnst and a 4×4 RST refer to transformsapplicable to a 4×4 region included in the transform coefficient blockwhen both W and H of the target block to are equal to or greater than 4,and the 4×4 region may be a top-left 4×4 region in the transformcoefficient block.

According to an embodiment of the present disclosure, for a transform inan encoding process, only 48 pieces of data may be selected and amaximum 16×48 transform kernel matrix may be applied thereto, ratherthan applying a 16×64 transform kernel matrix to 64 pieces of dataforming an 8×8 region. Here, “maximum” means that m has a maximum valueof 16 in an m×48 transform kernel matrix for generating m coefficients.That is, when an RST is performed by applying an m×48 transform kernelmatrix (m≤16) to an 8×8 region, 48 pieces of data are input and mcoefficients are generated. When m is 16, 48 pieces of data are inputand 16 coefficients are generated. That is, assuming that 48 pieces ofdata form a 48×1 vector, a 16×48 matrix and a 48×1 vector aresequentially multiplied, thereby generating a 16×1 vector. Here, the 48pieces of data forming the 8×8 region may be properly arranged, therebyforming the 48×1 vector. For example, a 48×1 vector may be constructedbased on 48 pieces of data constituting a region excluding the bottomright 4×4 region among the 8×8 regions. Here, when a matrix operation isperformed by applying a maximum 16×48 transform kernel matrix, 16modified transform coefficients are generated, and the 16 modifiedtransform coefficients may be arranged in a top-left 4×4 regionaccording to a scanning order, and a top-right 4×4 region and abottom-left 4×4 region may be filled with zeros.

For an inverse transform in a decoding process, the transposed matrix ofthe foregoing transform kernel matrix may be used. That is, when aninverse RST or LFNST is performed in the inverse transform processperformed by the decoding apparatus, input coefficient data to which theinverse RST is applied is configured in a one-dimensional vectoraccording to a predetermined arrangement order, and a modifiedcoefficient vector obtained by multiplying the one-dimensional vectorand a corresponding inverse RST matrix on the left of theone-dimensional vector may be arranged in a two-dimensional blockaccording to a predetermined arrangement order.

In summary, in the transform process, when an RST or LFNST is applied toan 8×8 region, a matrix operation of 48 transform coefficients intop-left, top-right, and bottom-left regions of the 8×8 region excludingthe bottom-right region among transform coefficients in the 8×8 regionand a 16×48 transform kernel matrix. For the matrix operation, the 48transform coefficients are input in a one-dimensional array. When thematrix operation is performed, 16 modified transform coefficients arederived, and the modified transform coefficients may be arranged in thetop-left region of the 8×8 region.

On the contrary, in the inverse transform process, when an inverse RSTor LFNST is applied to an 8×8 region, 16 transform coefficientscorresponding to a top-left region of the 8×8 region among transformcoefficients in the 8×8 region may be input in a one-dimensional arrayaccording to a scanning order and may be subjected to a matrix operationwith a 48×16 transform kernel matrix. That is, the matrix operation maybe expressed as (48×16 matrix)*(16×1 transform coefficient vector)=(48×1modified transform coefficient vector). Here, an n×1 vector may beinterpreted to have the same meaning as an n×1 matrix and may thus beexpressed as an n×1 column vector. Further, * denotes matrixmultiplication. When the matrix operation is performed, 48 modifiedtransform coefficients may be derived, and the 48 modified transformcoefficients may be arranged in top-left, top-right, and bottom-leftregions of the 8×8 region excluding a bottom-right region.

When a secondary inverse transform is based on an RST, the inversetransformer 235 of the encoding apparatus 200 and the inversetransformer 322 of the decoding apparatus 300 may include an inversereduced secondary transformer to derive modified transform coefficientsbased on an inverse RST on transform coefficients and an inverse primarytransformer to derive residual samples for the target block based on aninverse primary transform on the modified transform coefficients. Theinverse primary transform refers to the inverse transform of a primarytransform applied to a residual. In the present disclosure, deriving atransform coefficient based on a transform may refer to deriving thetransform coefficient by applying the transform.

The above-described non-separable transform, the LFNST, will bedescribed in detail as follows. The LFNST may include a forwardtransform by the encoding apparatus and an inverse transform by thedecoding apparatus.

The encoding apparatus receives a result (or a part of a result) derivedafter applying a primary (core) transform as an input, and applies aforward secondary transform (secondary transform).

y=G^(T)x   [Equation 9]

In Equation 9, x and y are inputs and outputs of the secondarytransform, respectively, and G is a matrix representing the secondarytransform, and transform basis vectors are composed of column vectors.In the case of an inverse LFNST, when the dimension of thetransformation matrix G is expressed as [number of rows×number ofcolumns], in the case of an forward LFNST, the transposition of matrix Gbecomes the dimension of G^(T).

For the inverse LFNST, the dimensions of matrix G are [48×16], [48×8],[16×16], [16×8], and the [48×8] matrix and the [16×8] matrix are partialmatrices that sampled 8 transform basis vectors from the left of the[48×16] matrix and the [16×16] matrix, respectively.

On the other hand, for the forward LFNST, the dimensions of matrix GTare [16×48], [8×48], [16×16], [8×16], and the [8×48] matrix andthe[8×16] matrix are partial matrices obtained by sampling 8 transformbasis vectors from the top of the [16×48] matrix and the [16×16] matrix,respectively.

Therefore, in the case of the forward LFNST, a [48×1] vector or [16×1]vector is possible as an input x, and a [16×1] vector or a [8×1] vectoris possible as an output y. In video coding and decoding, the output ofthe forward primary transform is two-dimensional (2D) data, so toconstruct the [48×1] vector or the [16×1] vector as the input x, aone-dimensional vector must be constructed by properly arranging the 2Ddata that is the output of the forward transformation.

FIG. 7 is a diagram illustrating a sequence of arranging output data ofa forward primary transformation into a one-dimensional vector accordingto an example. The left diagrams of (a) and (b) of FIG. 7 show thesequence for constructing a [48×1] vector, and the right diagrams of (a)and (b) of FIG. 7 shows the sequence for constructing a [16×1] vector.In the case of the LFNST, a one-dimensional vector×can be obtained bysequentially arranging 2D data in the same order as in (a) and (b) ofFIG. 7 .

The arrangement direction of the output data of the forward primarytransform may be determined according to an intra prediction mode of thecurrent block. For example, when the intra prediction mode of thecurrent block is in the horizontal direction with respect to thediagonal direction, the output data of the forward primary transform maybe arranged in the order of (a) of FIG. 7 , and when the intraprediction mode of the current block is in the vertical direction withrespect to the diagonal direction, the output data of the forwardprimary transform may be arranged in the order of (b) of FIG. 7 .

According to an example, an arrangement order different from thearrangement orders of (a) and (b) FIG. 7 may be applied, and in order toderive the same result (y vector) as when the arrangement orders of (a)and (b) FIG. 7 is applied, the column vectors of the matrix G may berearranged according to the arrangement order. That is, it is possibleto rearrange the column vectors of G so that each element constitutingthe x vector is always multiplied by the same transform basis vector.

Since the output y derived through Equation 9 is a one-dimensionalvector, when two-dimensional data is required as input data in theprocess of using the result of the forward secondary transformation asan input, for example, in the process of performing quantization orresidual coding, the output y vector of Equation 9 must be properlyarranged as 2D data again.

FIG. 8 is a diagram illustrating a sequence of arranging output data ofa forward secondary transform into a two-dimensional vector according toan example.

In the case of the LFNST, output values may be arranged in a 2D blockaccording to a predetermined scan order. (a) of FIG. 8 shows that whenthe output y is a [16×1] vector, the output values are arranged at 16positions of the 2D block according to a diagonal scan order. (b) ofFIG. 8 shows that when the output y is a [8×1] vector, the output valuesare arranged at 8 positions of the 2D block according to the diagonalscan order, and the remaining 8 positions are filled with zeros. X in(b) of FIG. 8 indicates that it is filled with zero.

According to another example, since the order in which the output vectory is processed in performing quantization or residual coding may bepreset, the output vector y may not be arranged in the 2D block as shownin FIG. 8 . However, in the case of the residual coding, data coding maybe performed in 2D block (eg, 4×4) units such as CG (Coefficient Group),and in this case, the data are arranged according to a specific order asin the diagonal scan order of FIG. 8 .

Meanwhile, the decoding apparatus may configure the one-dimensionalinput vector y by arranging two-dimensional data output through adequantization process or the like according to a preset scan order forthe inverse transformation. The input vector y may be output as theoutput vector×by the following equation.

x=Gy   [Equation 10]

In the case of the inverse LFNST, an output vector×can be derived bymultiplying an input vector y, which is a [16×1] vector or a [8×1]vector, by a G matrix. For the inverse LFNST, the output vector×can beeither a [48×1] vector or a [16×1] vector.

The output vector×is arranged in a two-dimensional block according tothe order shown in FIG. 7 and is arranged as two-dimensional data, andthis two-dimensional data becomes input data (or a part of input data)of the inverse primary transformation.

Accordingly, the inverse secondary transformation is the opposite of theforward secondary transformation process as a whole, and in the case ofthe inverse transformation, unlike in the forward direction, the inversesecondary transformation is first applied, and then the inverse primarytransformation is applied.

In the inverse LFNST, one of 8 [48×16] matrices and 8 [16×16] matricesmay be selected as the transformation matrix G. Whether to apply the[48×16] matrix or the [16×16] matrix depends on the size and shape ofthe block.

In addition, 8 matrices may be derived from four transform sets as shownin Table 2 above, and each transform set may consist of two matrices.Which transform set to use among the 4 transform sets is determinedaccording to the intra prediction mode, and more specifically, thetransform set is determined based on the value of the intra predictionmode extended by considering the Wide Angle Intra Prediction (WAIP).Which matrix to select from among the two matrices constituting theselected transform set is derived through index signaling. Morespecifically, 0, 1, and 2 are possible as the transmitted index value, 0may indicate that the LFNST is not applied, and 1 and 2 may indicate anyone of two transform matrices constituting a transform set selectedbased on the intra prediction mode value.

FIG. 9 is a diagram illustrating wide-angle intra prediction modesaccording to an embodiment of the present document.

The general intra prediction mode value may have values from 0 to 66 and81 to 83, and the intra prediction mode value extended due to WAIP mayhave a value from −14 to 83 as shown. Values from 81 to 83 indicate theCCLM (Cross Component Linear Model) mode, and values from −14 to −1 andvalues from 67 to 80 indicate the intra prediction mode extended due tothe WAIP application.

When the width of the prediction current block is greater than theheight, the upper reference pixels are generally closer to positionsinside the block to be predicted. Therefore, it may be more accurate topredict in the bottom-left direction than in the top-right direction.Conversely, when the height of the block is greater than the width, theleft reference pixels are generally close to positions inside the blockto be predicted. Therefore, it may be more accurate to predict in thetop-right direction than in the bottom-left direction. Therefore, it maybe advantageous to apply remapping, ie, mode index modification, to theindex of the wide-angle intra prediction mode.

When the wide-angle intra prediction is applied, information on theexisting intra prediction may be signaled, and after the information isparsed, the information may be remapped to the index of the wide-angleintra prediction mode. Therefore, the total number of the intraprediction modes for a specific block (eg, a non-square block of aspecific size) may not change, and that is, the total number of theintra prediction modes is 67, and intra prediction mode coding for thespecific block may not be changed.

Table 3 below shows a process of deriving a modified intra mode byremapping the intra prediction mode to the wide-angle intra predictionmode.

TABLE 3 Inputs to this process are: - a variable preModeIntra specifyingthe intra prediction mode, - a variable nTbW specifying the transformblock width, - a variable nTbH specifying the transform block height,- a variable cIdx specifying the colour component of the current block.Output of this process is the modified intra prediction modepredModeIntra. The variables nW and nH are derived as follows: - IfIntraSubPartitionsSplitType is equal to ISP_NO_SPLIT or cIdx is notequal to 0 the following applies:    nW =nTbW                            (8-97)    nH =nTbH                             (8-98) - Otherwise(IntraSubPartitionsSplitType is not equal to ISP_NO_SPLIT and cIdx isequal to 0 ), the   following applies:    nW =nCbW                            (8-99)    nH =nCbH                             (8-100) The variable  

 Ratio is set equal to Abs( Log2( nW : nH ) ) For non-square blocks (nWis not equal to nH), the intra prediction mode predModeIntra is modifiedas follows: - If all of the following conditions are true, predModeIntrais set equal tc ( predModeIntra − 65 )   - nW is greater than nH   -predModeIntra is greater than or equal to 2   - predModeIntra is lessthan ( whRatio > 1) ? ( 8 − 2 * whRatio ) :  

  - Otherwise, if all of the following conditions are true,predModeIntra is set equal to   - ( predModeIntra − 67 ).   - nH isgreater than nW   - predModeIntra is less than or equal to 66   -predModeIntra is greater than ( whRatio > 1 ) ? (60 − 2 * whRatio) : 60

indicates data missing or illegible when filed

In Table 3, the extended intra prediction mode value is finally storedin the predModeIntra variable, and ISP_NO_SPLIT indicates that the CUblock is not divided into sub-partitions by the Intra Sub Partitions(ISP) technique currently adopted in the VVC standard, and the cIdxvariable Values of 0, 1, and 2 indicate the case of luma, Cb, and Crcomponents, respectively. Log 2 function shown in Table 3 returns a logvalue with a base of 2, and the Abs function returns an absolute value.

Variable predModeIntra indicating the intra prediction mode and theheight and width of the transform block, etc. are used as input valuesof the wide angle intra prediction mode mapping process, and the outputvalue is the modified intra prediction mode predModeIntra. The heightand width of the transform block or the coding block may be the heightand width of the current block for remapping of the intra predictionmode. At this time, the variable whRatio reflecting the ratio of thewidth to the width may be set to Abs(Log 2(nW/nH)).

For a non-square block, the intra prediction mode may be divided intotwo cases and modified.

First, if all conditions (1)˜(3) are satisfied, (1) the width of thecurrent block is greater than the height, (2) the intra prediction modebefore modifying is equal to or greater than 2, (3) the intra predictionmode is less than the value derived from (8+2*whRatio) when the variablewhRatio is greater than 1, and is less than 8 when the variable whRatiois less than or equal to 1 [predModeIntra is less than (whRatio>1)?(8+2*whRatio): 8], the intra prediction mode is set to a value 65greater than the intra prediction mode [predModeIntra is set equal to(predModeIntra+65)].

If different from the above, that is, follow conditions (1)˜(3) aresatisfied, (1) the height of the current block is greater than thewidth, (2) the intra prediction mode before modifying is less than orequal to 66, (3) the intra prediction mode is greater than the valuederived from (60−2*whRatio) when the variable whRatio is greater than 1,and is greater than 60 when the variable whRatio is less than or equalto 1 [predModeIntra is greater than (whRatio>1)? (60−2*whRatio) : 60],the intra prediction mode is set to a value 67 smaller than the intraprediction mode [predModeIntra is set equal to (predModeIntra−67)].

Table 2 above shows how a transform set is selected based on the intraprediction mode value extended by the WAIP in the LFNST. As shown inFIG. 9 , modes 14 to 33 and modes 35 to 80 are symmetric with respect tothe prediction direction around mode 34. For example, mode 14 and mode54 are symmetric with respect to the direction corresponding to mode 34.Therefore, the same transform set is applied to modes located inmutually symmetrical directions, and this symmetry is also reflected inTable 2.

Meanwhile, it is assumed that forward LFNST input data for mode 54 issymmetrical with the forward LFNST input data for mode 14. For example,for mode 14 and mode 54, the two-dimensional data is rearranged intoone-dimensional data according to the arrangement order shown in (a) ofFIG. 7 and (b) of FIG. 7 , respectively. In addition, it can be seenthat the patterns in the order shown in (a) of FIG. 7 and (b) of FIG. 7are symmetrical with respect to the direction (diagonal direction)indicated by Mode 34.

Meanwhile, as described above, which transform matrix of the [48×16]matrix and the [16×16] matrix is applied to the LFNST is determined bythe size and shape of the transform target block.

FIG. 10 is a diagram illustrating a block shape to which the LFNST isapplied. (a) of FIG. 10 shows 4×4 blocks, (b) shows 4×8 and 8×4 blocks,(c) shows 4×N or N×4 blocks in which N is 16 or more, (d) shows 8×8blocks, (e) shows M×N blocks where M≤8, N≤8, and N>8 or M>8.

In FIG. 10 , blocks with thick borders indicate regions to which theLFNST is applied. For the blocks of FIGS. 10(a) and (b), the LFNST isapplied to the top-left 4×4 region, and for the block of FIG. 10(c), theLFNST is applied individually the two top-left 4×4 regions arecontinuously arranged. In (a), (b), and (c) of FIG. 10 , since the LFNSTis applied in units of 4×4 regions, this LFNST will be hereinafterreferred to as “4×4 LFNST”. As a corresponding transformation matrix, a[16×16] or [16×8] matrix may be applied based on the matrix dimensionfor G in Equations 9 and 10.

More specifically, the [16×8] matrix is applied to the 4×4 block (4×4 TUor 4×4 CU) of FIG. 10(a) and the [16×16] matrix is applied to the blocksin (b) and (c) of FIG. 10 . This is to adjust the computationalcomplexity for the worst case to 8 multiplications per sample.

With respect to (d) and (e) of FIG. 10 , the LFNST is applied to thetop-left 8×8 region, and this LFNST is hereinafter referred to as “8×8LFNST”. As a corresponding transformation matrix, a [48×16] matrix or[48×8] matrix may be applied. In the case of the forward LFNST, sincethe [48×1] vector (x vector in Equation 9) is input as input data, allsample values of the top-left 8×8 region are not used as input values ofthe forward LFNST. That is, as can be seen in the left order of FIG.7(a) or the left order of FIG. 7(b), the [48×1] vector may beconstructed based on samples belonging to the remaining 3 4×4 blockswhile leaving the bottom-right 4×4 block as it is.

The [48×8] matrix may be applied to an 8×8 block (8 ×8 TU or 8 ×8 CU) inFIG. 10(d), and the [48×16] matrix may be applied to the 8×8 block inFIG. 10(e). This is also to adjust the computational complexity for theworst case to 8 multiplications per sample.

Depending on the block shape, when the corresponding forward LFNST (4×4LFNST or 8×8 LFNST) is applied, 8 or 16 output data (y vector inEquation 9, [8×1] or [16×1] vector) is generated. In the forward LFNST,the number of output data is equal to or less than the number of inputdata due to the characteristics of the matrix G^(T).

FIG. 11 is a diagram illustrating an arrangement of output data of aforward LFNST according to an example, and shows a block in which outputdata of the forward LFNST is arranged according to a block shape.

The shaded area at the top-left of the block shown in FIG. 11corresponds to the area where the output data of the forward LFNST islocated, the positions marked with 0 indicate samples filled with 0values, and the remaining area represents regions that are not changedby the forward LFNST. In the area not changed by the LFNST, the outputdata of the forward primary transform remains unchanged.

As described above, since the dimension of the transform matrix appliedvaries according to the shape of the block, the number of output dataalso varies. As FIG. 11 , the output data of the forward LFNST may notcompletely fill the top-left 4×4 block. In the case of (a) and (d) ofFIG. 11 , a [16×8] matrix and a [48×8] matrix are applied to the blockindicated by a thick line or a partial region inside the block,respectively, and a [8×1] vector as the output of the forward LFNST isgenerated. That is, according to the scan order shown in (b) of FIG. 8 ,only 8 output data may be filled as shown in (a) and (d) of FIGS. 11 ,and 0 may be filled in the remaining 8 positions. In the case of theLFNST applied block of FIG. 10(d), as shown in FIG. 11(d), two 4×4blocks in the top-right and bottom-left adjacent to the top-left 4×4block are also filled with 0 values.

As described above, basically, by signaling the LFNST index, whether toapply the LFNST and the transform matrix to be applied are specified. Asshown FIG. 11 , when the LFNST is applied, since the number of outputdata of the forward LFNST may be equal to or less than the number ofinput data, a region filled with a zero value occurs as follows.

1) As shown in (a) of FIG. 11 , samples from the 8th and later positionsin the scan order in the top-left 4×4 block, that is, samples from the9th to the 16th.

2) As shown in (d) and (e) of FIG. 11 , when the [16×48] matrix or the[8×48] matrix is applied, two 4×4 blocks adjacent to the top-left 4×4block or the second and third 4×4 blocks in the scan order.

Therefore, if non-zero data exists by checking the areas 1) and 2), itis certain that the LFNST is not applied, so that the signaling of thecorresponding LFNST index can be omitted.

According to an example, for example, in the case of LFNST adopted inthe VVC standard, since signaling of the LFNST index is performed afterthe residual coding, the encoding apparatus may know whether there isthe non-zero data (significant coefficients) for all positions withinthe TU or CU block through the residual coding. Accordingly, theencoding apparatus may determine whether to perform signaling on theLFNST index based on the existence of the non-zero data, and thedecoding apparatus may determine whether the LFNST index is parsed. Whenthe non-zero data does not exist in the area designated in 1) and 2)above, signaling of the LFNST index is performed.

Since a truncated unary code is applied as a binarization method for theLFNST index, the LFNST index consists of up to two bins, and 0, 10, and11 are assigned as binary codes for possible LFNST index values of 0, 1,and 2, respectively. In the case of the LFNST currently adopted for VVC,a context-based CABAC coding is applied to the first bin (regularcoding), and a bypass coding is applied to the second bin. The totalnumber of contexts for the first bin is 2, when (DCT-2, DCT-2) isapplied as a primary transform pair for the horizontal and verticaldirections, and a luma component and a chroma component are coded in adual tree type, one context is allocated and another context applies forthe remaining cases. The coding of the LFNST index is shown in a tableas follows.

TABLE 4 binIdx Syntax element 0 1 2 3 4 >=5 lfnst_idx[ ][ ](tu_mts_idx[x0][y0] = = 

bypass

na na na &&  

  != SINGLE_TREE) ? 1 : 

indicates data missing or illegible when filed

Meanwhile, for the adopted LFNST, the following simplification methodsmay be applied.

(i) According to an example, the number of output data for the forwardLFNST may be limited to a maximum of 16.

In the case of (c) of FIG. 10 , the 4×4 LFNST may be applied to two 4×4regions adjacent to the top-left, respectively, and in this case, amaximum of 32 LFNST output data may be generated. when the number ofoutput data for forward LFNST is limited to a maximum of 16, in the caseof 4×N/N×4 (N≥16) blocks (TU or CU), the 4×4 LFNST is only applied toone 4×4 region in the top-left, the LFNST may be applied only once toall blocks of FIG. 10 . Through this, the implementation of image codingmay be simplified.

FIG. 12 shows that the number of output data for the forward LFNST islimited to a maximum of 16 according to an example. As FIG. 12 , whenthe LFNST is applied to the most top-left 4×4 region in a 4×N or N×4block in which N is 16 or more, the output data of the forward LFNSTbecomes 16 pieces.

(ii) According to an example, zero-out may be additionally applied to aregion to which the LFNST is not applied. In this document, the zero-outmay mean filling values of all positions belonging to a specific regionwith a value of 0. That is, the zero-out can be applied to a region thatis not changed due to the LFNST and maintains the result of the forwardprimary transformation. As described above, since the LFNST is dividedinto the 4×4 LFNST and the 8×8 LFNST, the zero-out can be divided intotwo types ((ii)-(A) and (ii)-(B)) as follows.

(ii)-(A) When the 4×4 LFNST is applied, a region to which the 4×4 LFNSTis not applied may be zeroed out. FIG. 13 is a diagram illustrating thezero-out in a block to which the 4×4 LFNST is applied according to anexample.

As shown in FIG. 13 , with respect to a block to which the 4×4 LFNST isapplied, that is, for all of the blocks in (a), (b) and (c) of FIG. 11 ,the whole region to which the LFNST is not applied may be filled withzeros.

On the other hand, (d) of FIG. 13 shows that when the maximum value ofthe number of the output data of the forward LFNST is limited to 16 asshown in FIG. 12 , the zero-out is performed on the remaining blocks towhich the 4×4 LFNST is not applied.

(ii)-(B) When the 8×8 LFNST is applied, a region to which the 8×8 LFNSTis not applied may be zeroed out. FIG. 14 is a diagram illustrating thezero-out in a block to which the 8×8 LFNST is applied according to anexample.

As shown in FIG. 14 , with respect to a block to which the 8×8 LFNST isapplied, that is, for all of the blocks in (d) and (e) of FIG. 11 , thewhole region to which the LFNST is not applied may be filled with zeros.

(iii) Due to the zero-out presented in (ii) above, the area filled withzeros may be not same when the LFNST is applied. Accordingly, it ispossible to check whether the non-zero data exists according to thezero-out proposed in (ii) over a wider area than the case of the LFNSTof FIG. 11 .

For example, when (ii)-(B) is applied, after checking whether thenon-zero data exists where the area filled with zero values in (d) and(e) of FIG. 11 in addition to the area filled with 0 additionally inFIG. 14 , signaling for the LFNST index can be performed only when thenon-zero data does not exist.

Of course, even if the zero-out proposed in (ii) is applied, it ispossible to check whether the non-zero data exists in the same way asthe existing LFNST index signaling. That is, after checking whether thenon-zero data exists in the block filled with zeros in FIG. 11 , theLFNST index signaling may be applied. In this case, the encodingapparatus only performs the zero out and the decoding apparatus does notassume the zero out, that is, checking only whether the non-zero dataexists only in the area explicitly marked as 0 in FIG. 11 , may performthe LFNST index parsing.

Alternatively, according to another example, the zero-out may beperformed as shown in FIG. 15 . FIG. 15 is a diagram illustrating thezero-out in a block to which the 8×8 LFNST is applied according toanother example.

As shown in FIGS. 13 and 14 , the zero-out may be applied to all regionsother than the region to which the LFNST is applied, or the zero-out maybe applied only to a partial region as shown in FIG. 15 . The zero-outis applied only to regions other than the top-left 8×8 region of FIG. 15, the zero-out may not be applied to the bottom-right 4×4 block withinthe top-left 8×8 region.

Various embodiments in which combinations of the simplification methods((i), (ii)-(A), (ii)-(B), (iii)) for the LFNST are applied may bederived. Of course, the combinations of the above simplification methodsare not limited to the following embodiments, and any combination may beapplied to the LFNST.

Embodiment

Limit the number of output data for forward LFNST to a maximum of 16→(i)

When the 4×4 LFNST is applied, all areas to which the 4×4 LFNST is notapplied are zero-out→(ii)-(A)

When the 8×8 LFNST is applied, all areas to which the 8×8 LFNST is notapplied are zero-out→(ii)-(B)

After checking whether the non-zero data exists also the existing areafilled with zero value and the area filled with zeros due to additionalzero outs ((ii)-(A), (ii)-(B)), the LFNST index is signaled only whenthe non-zero data does not exist→(iii)

In the case of Embodiment, when the LFNST is applied, an area in whichthe non-zero output data can exist is limited to the inside of thetop-left 4×4 area. In more detail, in the case of FIG. 13(a) and FIG.14(a), the 8th position in the scan order is the last position wherenon-zero data can exist. In the case of FIGS. 13(b) and (c) and FIG.14(b), the 16th position in the scan order (ie, the position of thebottom-right edge of the top-left 4×4 block) is the last position wheredata other than 0 may exist.

Therefore, when the LFNST is applied, after checking whether thenon-zero data exists in a position where the residual coding process isnot allowed (at a position beyond the last position), it can bedetermined whether the LFNST index is signaled.

In the case of the zero-out method proposed in (ii), since the number ofdata finally generated when both the primary transform and the LFNST areapplied, the amount of computation required to perform the entiretransformation process can be reduced. That is, when the LFNST isapplied, since zero-out is applied to the forward primary transformoutput data existing in a region to which the LFNST is not applied,there is no need to generate data for the region that become zero-outduring performing the forward primary transform. Accordingly, it ispossible to reduce the amount of computation required to generate thecorresponding data. The additional effects of the zero-out methodproposed in (ii) are summarized as follows.

First, as described above, the amount of computation required to performthe entire transform process is reduced.

In particular, when (ii)-(B) is applied, the amount of calculation forthe worst case is reduced, so that the transform process can belightened. In other words, in general, a large amount of computation isrequired to perform a large-size primary transformation. By applying(ii)-(B), the number of data derived as a result of performing theforward LFNST can be reduced to 16 or less. In addition, as the size ofthe entire block (TU or CU) increases, the effect of reducing the amountof transform operation is further increased.

Second, the amount of computation required for the entire transformprocess can be reduced, thereby reducing the power consumption requiredto perform the transform.

Third, the latency involved in the transform process is reduced.

The secondary transformation such as the LFNST adds a computationalamount to the existing primary transformation, thus increasing theoverall delay time involved in performing the transformation. Inparticular, in the case of intra prediction, since reconstructed data ofneighboring blocks is used in the prediction process, during encoding,an increase in latency due to a secondary transformation leads to anincrease in latency until reconstruction. This can lead to an increasein overall latency of intra prediction encoding.

However, if the zero-out suggested in (ii) is applied, the delay time ofperforming the primary transform can be greatly reduced when LFNST isapplied, the delay time for the entire transform is maintained orreduced, so that the encoding apparatus can be implemented more simply.

Hereinafter, the image decoding process in which the embodiment isreflected is shown in a table.

TABLE 5 7.3.2.3 Sequence parameter set RBSP syntax Descriptorseq_parameter_set_rbsp( ) {  ...... sps_log2_max_luma_transform_size_minus5 u( 

 )  sps_sao_enabled_flag u( 

 )  sps_alf_enabled_flag u( 

 )  sps_ pcm_enabled_flag u( 

 )  ...... } 7.4.3.3 Sequence parameter set RBSP semantics  ...... MinTbLog2SizeY = 2 (7-14)  MaxTbLog2SizeY =sps_log2_max_luma_transform_size_minus5 − 5 (7-15)  MinTbSizeY = 1 <<MinTbLog2SizeY (7-16)  MaxTbSizeY = 1 << MaxTbLog2SizeY (7-17) ......sps_log?_max_luma_transform_size_minus5 specifies the base 2 logarithmof the maximum transform size minus 5. ...... sps_sbt_enabled_flag equalto 0 specifies that subblock transform for inter-predicted CUs isdisabled. sps_sbt_enabled_flag equal to 1 specifies that subblocktransform for inter-predicteds CU is enabled. sps_sbt_max_size_64_flagequal to 0 specifies that the maximum CU width and height for allowingsubblock transform is 32 luma samples. sps_sbt_max_size_64_flag equal to1 specifies that the maximum CU width and height for allowing subblocktransform is 64 luma samples.  MaxSbtSize = Min( MaxTbSizeY,sps_sbt_max_size_64_flag ? 64 : 32) (7-34)

indicates data missing or illegible when filed

Table 5 shows that sps_log 2_max_luma_transform_size_minus5, which issyntax information on the size of a transform block, is signaled throughthe sequence parameter set syntax. According to semantics, sps_log2_max_luma_transform_size_minus5 represents a value obtained bysubtracting 5 after taking the base 2 logarithm for the maximumtransform size.

The minimum size (MinTbSizeY) of a transform block in whichtransformation can be performed is set to 4 (MinTbSizeY=1<<MinTbLog2SizeY), and the maximum size of a transform block in whichtransformation can be performed may be derived as a power of 2 of avalue obtained by adding 5 to sps_log2_max_luma_transform_size_minus5(MaxTbLog 2SizeY sps_log2_max_luma_transform_size_minus5+5, MaxTbSizeY=1 MaxTbLog 2SizeY).

Since sps_log 2_max_luma_transform_size_minus5 consists of 1 bit and hasa value of 0 or 1, the width and height of the maximum transform blockmay be set to 32 or 64 based on sps_log 2_max_luma_transform_size_minus5of Table 5.

Meanwhile, according to another embodiment, flag informationsps_max_luma_transform_size_64_flag for the size of the maximumtransform block may be signaled. Whensps_max_luma_transform_size_64_flag is 1, the maximum size of thetransform block is 64, and when sps_max_luma_transform_size_64 flag is0, the maximum size of the transform block is 32.

TABLE 6 7.3.7.5 Coding unit syntax Descriptor coding_unit( x0, y0,cbWidth, cbHeight, treeType ) {  ......  if( !pcm_flag[ x0 ][ y0 ] ) {  if( CuPredMode[ x0 ][ y0 ] := MODE_INTRA &&    general_merge_flag[ x0][ y0 ] = = 0 )    cu_cbf ae( 

 )   if( cu_cbf ) {    ......    LfnstDcOnly = 1   LfnstZeroOutSigCoeffFlag = 1    transform_tree( x0, y0, cbWidth,cbHeight, treeType )    lfnstWidth =  

  treeType = = DUAL_IREE_CHROMA ) ? cbWidth SubWidthC       : cbWidth   lfnstHeight = ( treeType = = DUAL_TREE_CHROMA ) ? cbHeight  

     SubHeightC       : cbHeight    if Min( lfnstWidth, lfnstHeight ) >=4 && sps_lfnst_enabled_flag = = 1 &&     CuPredMode[ x0 ][ y0 ] = =MODE_INTRA &&     IntraSubPartitionsSplitType = = ISP_NO_SPLIT &&    !intra_mip_flag[ x0 ][ y0 ] && tu_mts_idx[ x0 ][ y0 ] = = 0 && Max(cbWidth, cbHeight ) <= MaxTbSizeY )  

      if( LfnstDcOnly = = 0 && LfnstZeroOutSigCoeffFlag = = 1 )     lfnst_idx[ x0 ][ y0 ] ae( 

 )    }   }  } }

indicates data missing or illegible when filed

Table 6 shows lfnst_idx[x0][y0] syntax elements signaled at the codingunit level. lfnst_idx[x0][y0] may indicate any one of two transformkernel matrices included in the transform set. If lfnst_idx is 0, it mayindicate that non-separable secondary transform, that is, LFNST is notapplied.

In order for lfnst_idx to be parsed by the decoding apparatus, manyconditions must be satisfied. First, the variable LfnstDcOnly and thevariable LfnstZeroOutSigCoeffFlag are initially set to 1. After parsingthe syntax for the transformation tree (transform tree(x0, y0, cbWidth,cbHeight, treeType)), when the variable LfnstDcOnly set to 1 is changedto 0, and the value of the variable LfnstZeroOutSigCoeffFlag ismaintained at 1, lfnst_idx can be parsed [if(LfnstDcOnly==0 &&LfnstZeroOutSigCoeffFlag==1)]. The variable LfnstDcOnly and the variableLfnstZeroOutSigCoeffFlag may be derived through residual coding syntaxinformation.

Meanwhile, the maximum coding block size in which lfnst_idx[x0][y0] canbe coded is limited to the maximum transform size (Max(cbWidth,cbHeight)<=MaxTbSizeY).

In addition, since the width (cbWidth) of the coding block and theheight (cbHeight) of the coding block indicate the width of the codingblock and the height of the coding block for the luma component,respectively, in the case of the chroma component, the LFNST may beapplied to each block having a smaller size according to the image colorformat (eg, 4:2:0).

Specifically, as shown in Table 6, if the tree type of the target blockis dual tree chroma, the LFNST may be applied to a chroma block having asize divided by SubWidthC and SubHeight indicating a variable for thechroma format in the size of the luma coding block[lfnstWidth=(treeType==DUAL_TREE_CHROMA)? cbWidth/SubWidthC : cbWidth,lfnstHeight=(treeType==DUAL_TREE_CHROMA)? cbHeight/SubHeightC :cbHeight].

If the color format is 4:2:0, SubWidthC and SubHeight become 2, so theLFNST may be applied to a chroma block having a width and heightobtained by dividing the width and height of the luma block by 2.Therefore, since the LFNST can be applied when the size of the lumablock is equal to or smaller than the 64×64 block, the LFNST can beapplied when the size of the chroma block is equal to or smaller thanthe 32×32 block when the color format is 4:2:0.

Meanwhile, in this document, when the horizontal and vertical lengths ofblock A are Wa and Ha, respectively, and when the horizontal andvertical lengths of block B are Wb and Hb, respectively, block A issmaller than block B means that Wa is equal to or smaller than Wb, Ha isequal to or smaller than Hb, and Wa and Wb are not equal or Ha and Hbare not equal. Also, the meaning that block A is smaller than or equalto block B indicates that Wa is equal to or smaller than Wb and Ha isequal to or smaller than Hb.

In summary, when the size of the target block is equal to or smallerthan the preset maximum size, the LFNST may be applied, this maximumsize may be applied to the size of the luma block, and correspondingly,the maximum size of the chroma block to which the LFNST may be appliedmay be derived.

TABLE 7 7.3.7.10 Transform unit syntax Descriptor transform_unit( x0,y0, tbWidth, tbHeight treeType, subTuIndex ) {  ......  if( tu_cbf_luma[x0 ][ y0 ] && treeType != DUAL_TREE_CHROMA    && (tbWidth <= 32 ) && (tbHeight <= 32 )    && (IntraSubPartitionsSplit[ x0 ][ y0 ] = =ISP_NO_SPLIT ) && (!cu_sbt_flag ) ) {   if( transform_skip_enabled_flag&& tbWidth <= MaxTsSize && tbHeight <= MaxTsSize )  transform_skip_flag[x0 ][ y0 ] ae( 

 )   if( (( CuPredMode[ x0 ][ y0 ] = = MODE_INTER &&sps_explicit_mt_inter_enabled_   flag )     | | ( CuPredMode [ x0 ][ y0] = = MODE_INTRA && sps_explicit_mts_intra_     enabled_flag ))     && (!transform_skip_flag[ x0 ][ y0 ] ) )     tu_n 

 _idx[ x0 ][ y0 ] ae( 

 )  }  ...... } 7.4.3.10 Transform unit semantics ......transform_skip_flag[ x0 ][ y0 ] specifies whether a transform is appliedto the luma trans form block or not. The array indices x0, y0 specify⁻the location ( x0, y0 ) of the top-left luma sample of the consider edtransform block relative to the top-left luma sample of the picture.transform_skip_flas[ x0 ][ y0 ] eq ual to 1 specifies that no transformis applied to the luma transform block. transform_skip_flag[ x0 ][ y 0 ]equal to 0 specifies that the decision whether transform is applied tothe luma transform block or not depends on other syntax elements. Whentransform_skip_flag[ x0 ][ y0 ] is not present, it is inferred asfollows: - IfBdcpmFlag[ x0 ][ x0 ] is equal to 1, transform_skip_flag[x0 ][ y0 ] is inferred to be equal to 1. - Otherwise (BdcpmFlag[ x0 ][x0 ] is equal to 0), transform_skip_flag[ x0 ][ y0 ] is inferred to beequal to 0. ......

indicates data missing or illegible when filed

Table 7 shows transform_skip_flag indicating whether to skip transformwith respect to a transform block and tu_mts_idx[x0][y0], which istransform kernel index information for primary transform.

As shown in Table 7, in order for tu_mts_idx[x0][y0] to be signaled,there may be a case where the prediction mode of the current block isinter mode or or when flag informationsps_explicit_mts_inter_enabled_flag that explicitly indicates whetherthe MTS can be applied to residual data generated by the interprediction is 1 [(CuPredMode[x0][y0]==MODE_INTER &&sps_explicit_mts_inter_enabled_flag)], or a case where the predictionmode of the current block is intra mode or or when flag informationsps_explicit_mts_intra_enabled_flag that explicitly indicates whetherthe MTS can be applied to residual data generated by the intraprediction is 1 [(CuPredMode[x0][y0]==MODE_INTRA &&sps_explicit_mts_intra_enabled_flag)].

Additionally, when a condition in which transform_skip_flag is not 0 issatisfied, tu_mts_idx[x0][y0] may be parsed.

Meanwhile, according to another example, the tu_mts_idx[x0][y0] may besignaled at the coding unit level of Table 6 rather than the transformunit level.

TABLE 8 7.3.7.11 Residual coding syntax Descriptor residualcoding( x0,y0, logTbWidth log2TbHeight, cIdx ) {  if( ( tu_mts_idx[ x0 ][ y0 ] > 0   ( cu_sbt_flag && log2TbWidth < 6 && log2TbHeight < 6 ) )     && cIdx= = 0 && log2TbWidth > 4 )   log2ZoTbWidth = 4  else   log2ZoTbWidth =Min( log2Tb Width, 5 )  MaxCobs =2*(1 << log2TbWidth ) * ( 1 <<log2TbHeight )  if( tu_mts_idx[ x0][ y0] > 0 | |    ( cu_sbt_flag &&log2TbWidth < 6 && log2TbHeight < 6 ) )     && cIdx = = 0 &&log2TbHeight > 4)   log2ZoTtHeight = 4  else   log2ZoTtHeight = Minlog2TbHeight, 5 )  if( log2TbWidth > 0 )   last_sig_coeff_x_prefix ae(v) if( log2TbHeight > 0 )   last_sig_coeff_y_prefix ae(v)  if(last_sig_coeff_x_prefix > 3)   last_sig_coeff_x_suffix ae(v)  if(last_sig_coeff_y_prefix > 3)   last_sig_coeff_y_suffix ae(v) log2TbWidth = log2ZoTbWidth  log2TbHeight = log2ZoTbHeight  log2SbW = (Min( log2TbWidth, log2TbHeight ) < 2 ? 1 : 2 )  log2StH = log2SbW  if(log2TbWidth − log2TbHeight > 3 ) {   if( log2TbWidth < 2 ) {    log2SbW= log2TbWidth    log2SbH = 4 − log2SbW   } else if( log2TbHeight < 2 ) {   log2SbH = log2TbHeight    log2SbW = 4 − log2SbH   }  }  numSbCoeff =1 << ( log2SbW − log2SbH )  lastScanPos = numSbCoeff  lastSubBlock = ( 1<< ( log2TbWidth − log2TbHeight − (log2SbW − log2SbH  ) ) ) − 1  do {  if lastScanPos = = 0 ) {    lastScanPos = numSbCoeff    lastSubBlock−−   }   lastScanPos− −   xs = DiagScanOrder[ log2TbWidth − log2SbW ][log2TbHeight − log2SbH ]     [ last SubBlock ][ 0 ]   ys =DiagScanOrder[ log2TbWidth − log2SbW ][ log2TbHeight − log2SbH ]     [last SubBlock ][ 1 ]   xC = ( xS << log2SbW ) − DiagScanOrder[ log 

 SbW ][ log 

 SbH ]   [ lastScanPos ][ 0 ]   yC = ( yS << log2SbH ) − DiagScanOrder[log 

 SbW ][ log 

 SbH ]   [ lastScanPos ][ 1 ]  } while( ( xC != LastSignificantCoeffX )(yC != LastSignificantCoeffY ) )  if( lastSubBlock = = 0 &&log2TbWidth >=    && log2TbHeight >= 2 &&   !transform_skip_flag[ x0 ][y0 ] && lastScanPos > 0 ) {   LfnstDcOnly = 0  }  if( ( lastSubBlock > 0&& log2Tb Width >= 2 && log 

 TbHeight >= 2 ) | |   ( lastScanPos > 7 && ( log2Tb Width = = 2 | |log2TbHeight = = 3 ) &&   log2TbWidth = = log2TbHeight ) ) {  LfnstZeroOutSigCoeffFlag = 0  }  ...... }

indicates data missing or illegible when filed

Table 8 shows a residual coding syntax, and the process in which thevariable LfnstDcOnly and the variable LfnstZeroOutSigCoeffFlag of Table6 are derived is shown.

Based on the size of the transform block, a variable log 2SbW and avariable log 2SbH indicating the height and width of the sub-block canbe derived, numSbCoeff representing the number of coefficients that mayexist in a sub-block may be set based on the variable log 2SbW and thevariable log 2SbH [numSbCoeff=1<<(log 2SbW+log 2SbH)].

A variable lastScanPos indicating the position of the last significantcoefficient within the subblock is initially set to numSbCoeff, avariable lastSubBlock indicating the subblock in which the last non-zerocoefficient exists is initially set to “(1<<(log 2TbWidth+log2TbHeight−(log 2SbW+log 2SbH)))−1”.

While scanning diagonally in the subblock corresponding to lastSubBlock[lastScanPos−−], it is checked whether the last non-zero significantcoefficient exists at the corresponding position.

When no significant coefficient is found until the variable lastScanPosbecomes 0 within the subblock pointed to by lastSubBlock, the variablelastScanPos is again set to numSbCoeff, and the variable lastSubBlock isalso changed to the next sub-block in the scan direction.

That is, as the variable lastScanPos and the variable lastSubBlock areupdated according to the scan direction, the position where the lastnon-zero coefficient exists is identified.

The variable LfnstDcOnly indicates whether a non-zero coefficient existsat a position that is not a DC component for at least one transformblock in one coding unit, when the non-zero coefficient exists in theposition that is not the DC component for at least one transform blockin the one coding unit, it becomes 0, and when non-zero coefficients donot exist at positions other than the DC components for all transformblocks in the one coding unit it becomes 1. In this document, the DCcomponent refers to (0, 0) or the top-left position relative to the 2Dcomponent.

Several transform blocks may exist within one coding unit. For example,in the case of a chroma component, transform blocks for Cb and Cr mayexist, and in the case of a single tree type, transform blocks for luma,Cb, and Cr may exist. According to an example, when a non-zerocoefficient other than the position of the DC component is found in onetransform block among transform blocks constituting the current codingblock, the variable LnfstDcOnly value may be set to 0.

Meanwhile, since the residual coding is not performed on thecorresponding transform block if the non-zero coefficient do not existin the transform block, the value of the variable LfnstDcOnly is notchanged by the corresponding transform block. Therefore, when thenon-zero coefficient does not exist in the position that is not the DCcomponent in the transform block, the value of the variable LfnstDcOnlyis not changed and the previous value is maintained. For example, if thecoding unit is coded as a single tree type and the variable LfnstDcOnlyvalue is changed to 0 due to the luma transform block, when the non-zerocoefficient exist only in the DC component in the Cb transform block orthe non-zero coefficient do not exist in the Cb transform block, thevalue of the variable LfnstDcOnly remains 0. The value of the variableLfnstDcOnly is initially initialized to 1, and if no component in thecurrent coding unit can update the value of the variable LfnstDcOnly to0, it maintains the value of 1 as it is and when the value of thevariable LfnstDcOnly is updated to 0 at any one of the transform blocksconstituting the corresponding coding unit, it is finally maintained at0.

As shown in Table 8, when the index of the subblock in which the lastnon-zero coefficient exists is 0 [lastSubBlock==0] and the position ofthe last non-zero coefficient in the sub-block is greater than 0[lastScanPos>0], the variable LfnstDcOnly may be derived as 0. Thevariable LfnstDcOnly can be derived as 0 only when the width and heightof the transform block are 4 or more [log 2TbWidth>=2 && log2TbHeight>=2], and no transform skip is applied[!transform_skip_flag[x0][y0]].

Assuming that the LFNST is applied, the variableLfnstZeroOutSigCoeffFlag, which can indicate whether the zero-out wasperformed properly, is set to 0 in case that the index of the sub-blockin which the last non-zero coefficient exists is greater than 0, and thewidth and height of the transform block are both greater than or equalto 4 [(lastSubBlock>0 && log 2TbWidth>=2 && log 2TbHeight>=2)], or incase that when the last position of the non-zero coefficient within thesubblock in which the last non-zero coefficient exists is greater than 7and the size of the transform block is 4×4 or 8×8 [(lastScanPos>7 &&(log 2TbWidth==2 log 2TbHeight==3) && log 2TbWidth==log 2TbHeight)].

That is, the first condition for the variable LfnstZeroOutSigCoeffFlagis a condition in which the non-zero coefficient is derived in theregion other than the top-left region to which the LFNST can be appliedin the transform block (That is, when the significant coefficient insub-blocks other than the top-left sub-block (4×4) are derived). Whenthe first condition is satisfied, the flag variablelfnstZeroOutSigCoeffFlag for the zero out of the LFNST is set to 0.Satisfying the first condition indicates that zero-out is not performed,assuming that that LFNST is applied.

The second condition for the variable LfnstZeroOutSigCoeffFlag is forthe 4×4 block and the 8×8 block. When the LFNST is applied to the 4×4block and the 8×8 block, since the last position where the non-zerocoefficient can exist is the 8th position as shown in (a) and (d) ofFIG. 11 , if the non-zero coefficient exists outside the 7th positionwhen starting from 0, the flag variable lfnstZeroOutSigCoeffFlag is setto 0. Satisfying the second condition also indicates that zero-out isnot performed when it is assumed that the LFNST is applied.

As such, when the flag variable lfnstZeroOutSigCoeffFlag is set to 0, asshown in Table 6, lfnst_idx signaled at the coding unit level is notsignaled. That is, when the flag variable lfnstZeroOutSigCoeffFlag isset to 0, the decoding apparatus does not parse lfnst_idx.

In summary, at the coding unit level, the variable LfnstDcOnly and thevariable LfnstZeroOutSigCoeffFlag are set to 1, respectively, and thenare newly derived through the process shown in Table 8 at the residualcoding level. Only when the variable LfnstDcOnly derived from theresidual coding level is 0 and the variable LfnstZeroOutSigCoeffFlag is1 [if(LfnstDcOnly==0 && LfnstZeroOutSigCoeffFlag==1), lfnst_idx may besignaled.

TABLE 9 8.4.5 Decoding process for intra blocks 8.4.5.1 General decodingprocess for intra blocks Inputs to this process are: - a sample location(xTb0, yTb0) specifying the top-left sample of the current transformblock   relative to the top-left sample of the current picture, - avariable nTbW specifying the width of the current transform block, - avariable nTbH specifying the height of the current transform block, - avariable predModeIntra specifying the intra prediction mode, - avariable cIdx specifying the colour component of the current block.Output of this process is a modified reconstructed picture beforein-loop filtering. The maximum transform block size maxTbSize is derivedas follows:    maxTbWidth = (cIdx = = 0) ? MaxTbSizeY : MaxTbSizeY /SubWidthC    maxTbHeight = (cIdx = = 0 ) ? MaxTbSizeY : MaxTbSizeY /SubHeightC The luma sample location is derived as follows:    (xTbY,yTbY) = ( cIdx = = 0) ? ( xTb0, yTb0 ) : (xTb0 * SubWidthC, yTb0 *SubHeight    C)(8-50) Depending on maxTbSize, the following applies:- If IntraSubPartitionsSplitType is equal to NO_ISP_SPLIT and nTbW isgreater than maxTb Width   or nTbH is greater than maxTbHeight, thefollowing ordered steps apply.   1. The variables newTbW and newTbH arederived as follows:     newTbw = ( nTbW > maxTb Width) ? (nTbW / 2) :nThW (8-51)     newTbH = ( nTbH > maxTbHeight) ? ( nTbH / 2 ) : nTbH(8-52)   2. The general decoding process for intra blocks as specifiedin this clause is invoked with the     location ( xTb0, yTb0 ), thetransform block width nTbW set equal to newTbW and the     height nTbHset equal to newTbH, the intra prediction mode predModeIntra and thevariable     cIdx as inputs, and the output is a modified reconstructedpicture before in-loop filtering.   3. If nTbW is greater thanmaxTbWidth, the general decoding process for intra blocks as    specified in this clause is invoked with the location (xTb0, yTb0)set equal to     ( xTb0 + newTbW, yTb0 ) the transform block width nTbWset equal to newTbW and the     height nTbH set equal to newTbH, theintra prediction mode predModeIntra and the variable     cIdx as inputs,and the output is a modified reconstructed picture before in-loopfiltering.   4. If nTbH is greater than maxTbHeight, the generaldecoding process for intra blocks as     specified in this clause isinvoked with the location (xTb0, yTb0) set equal to     ( xTb0, yTb0 −newTbH ). the transform block width nTbW set equal to newTbW and the    height nTbH set equal to newTbH, the intra prediction modepredModeIntra and the variable     cIdx as inputs, and the output is amodified reconstructed picture before in-loop filtering.   5. If nTbW isgreater than maxTbWidth and nTbH is greater than maxTbHeight, thegeneral     decoding process for intra blocks as specified in thisclause is invoked with the location     ( xTb0, yTb0 ) set equal to (xTb0 − newTbW, yTb0 − newTbH ), the transform block width     nTbW setequal to newTbW and the height nTbH set equal to newTbH, the intraprediction     mode predModeIntra, and the variable cIdx as inputs, andthe output is a modified     reconstructed picture before in-loopfiltering. - Otherwise, the following ordered steps apply: ......

TABLE 10 8.5.8 Decoding process for the residual signal of coding blockscoded in inter prediction mode Inputs to this process are: - a samplelocation (xTb0, yTb0) specifying the top-left sample of the currenttransform block relative to the top-left sample of the current picture,- a variable nTbW specifying the width of the current transform block,- a variable nTbH specifying the height of the current transform block,- a variable cIdx specifying the colour component of the current block.Output of this process is an (nTbW)x(nTbH) array resSamples. The maximumtransform block size maxTbSize is derived as follows:    maxTbWidth =(cIdx = = 0) ? MaxTbSizeY : MaxTbSizeY / SubWidthC    maxTbHeight =(cIdx = = 0) ? MaxTbSizeY : MaxTbSizeY / SubHeightC The luma samplelocation is derived as follows:   ( xTbY, yTbY ) = ( cIdx = = 0 ) ? (xTb0, yTb0 ) : ( xTb0 * SubWidthC, yTb0 * SubHeightC )     (8-868)Depending on maxTbSize, the following applies: - IfnTbW is greater thanmaxTbWidth or nTbH is greater than maxTbHeight, the following ordered  steps apply.   1. The variables newTbW and newTbH are derived asfollows:     newTbW = ( nTbW > maxTbWidth) ? ( nTbw / 2) : nTbW (8-869)    newTbH = ( nTbH > maxTbHeight) ? (nTbH / 2 ) : nTbH (8-870)   2. Thedecoding process process for the residual signal of coding units codedin inter prediction     mode as specified in this clause is invoked withthe location ( xTb0, yTb0 ), the transform     block width nTbW setequal to newTbW and the height nTbH set equal to newTbH and the    variable cIdx as inputs, and the output is a modified reconstructedpicture before in-loop     filtering.   3. When nTbW is greater thanmaxTbWidth, the decoding process process for the residual     signal ofcoding units coded in inter prediction mode as specified in this clauseis invoked     with the location ( xTb0, yTb0 ) set equal to (xTb0 −newTbW, yTb0 ) the transform block     width nTbW set equal to newTbWand the height nTbH set equal to newTbH, and the variable     cIdx asinputs, and the output is a modified reconstructed picture .   4. WhennTbH is greater than maxTbHeight, the decoding process process for theresidual     signal of coding units coded in inter prediction mode asspecified in this clause is invoked     with the location ( xTb0, yTb0 )set equal to ( xTb0, yTb0 + newTbH ) the transform block     width nTbWset equal to newTbW and the height nTbH set equal to newTbH, and thevariable     cIdx as inputs, and the output is a modified reconstructedpicture before in-loop filtering.   5. Wwhen nTbW is greater thanmaxTbWidth and nTbH is greater than maxTbHeight, the     decodingprocess process for the residual signal of coding units coded in interprediction     mode as specified in this clause is invoked with thelocation ( xTb0, yTb0 ) set equal to     ( xTb0 + newTbW, yTb0 − newTbH) the transform block width nTbW set equal to     newTbW and height nTbHset equal to newTbH, and the variable cIdx as inputs, and the     outputis a modified reconstructed picture before in-loop filtering. Otherwise,the scaling and transformation process as specified in clause 8.7.2 isinvoked with the luma location ( xTbY, yTbY ), the variable cIdx, thetransform width nTbW and the transform height nTbH as inputs, and theoutput is an ( nTbW)x(nTbH) array resSamples.

Tables 9 and 10 show that intra prediction and inter predictionprocesses are performed based on the variable MaxTbSizeY for the size ofthe transform block derived from Table 5.

The maximum width (maxTbWidth) and maximum height (maxTbHeight) of thetransform block are derived from either the variable MaxTbSizeY orMaxTbSizeY/SubWidthC that reflects the color format according to thecolor index cIdx for luma or chroma [maxTbWidth=(cIdx==0) ? MaxTbSizeY :MaxTbSizeY/SubWidthC, maxTbHeight=(cIdx==0) ? MaxTbSizeY :MaxTbSizeY/SubHeightC].

The height and width of the transform block for the inter prediction andthe intra prediction are set based on the variable maxTbWidth and thevariable maxTbHeight derived in this way [newTbW=(nTbW>maxTbWidth) ?(nTbW/2) : nTbW, newTbH=(nTbH>maxTbHeight) ? (nTbH/2): nTbH], asubsequent prediction process may be performed based on the set value.

TABLE 11 8.7.4 Transformation process for scaled transform coefficients8.7.4.1 General Inputs to this process are: - a luma location (xTbY,yTbY) specifying the top-left sample of the current luma transform  block relative to the top-left luma sample of the current picture, - avariable nTbW specifying the width of the current transform block, - avariable nTbH specifying the height of the current transform block, - avariable cIdx specifying the colour component of the current block, - an(nTbW)x(nTbH) array d[ x ][ y ] of scaled transform coefficients with x= 0..nTbW − 1, y = 0..nTbH − 1. Output of this process is the(nTbW)x(nTbH) array r[ x ][ y ] of residual samples with x = 0..nTbW −1, y = 0..nTbH − 1. When lfnst_idx[ xTbY ][ yTbY ] is not equal to 0 andboth nTbW and nTbH are greater than or equal to 4, the followingapplies: - The variables predModeIntra, nLfnstOutSize, log2LfnstSize,nLfnstSize, and nonZeroSize are   derived as follows:    predModeIntra =   (cIdx = = 0 ) ? IntraPredModeY[ xTbY ][ yTbY ] : IntraPredModeC[ xTbY][ yTbY ] (8-9    52)    nLfnstOutSize = ( nTbW >= 8 && nTbH >= 8 ) ? 48: 16 (8-953)    log2LfnstSize = ( nTbW >= 8 && nTbH >= 8 ) ? 3 : 2(8-954)    nLfnstSize = 1 << log2LfnstSize (8-955)    nonZeroSize = ( (nTbW = = 4 && nTbH = = 4 ) | | (8-958)    ( nTbW = = 8 && nTbH = = 8 ) )? 8 : 16 - When predModeIntra is greater than or equal to 81, the chromaintra prediction mode   derivation process as specified in clause 8.4.4is invoked with a luma location ( xTbY, yTbY ),   nTbW, nTbH as inputs,and predModeIntra is set equal to   IntraPredModeY[ xTbY + nTbW / 2 ][yTbY + nTbH / 2 ]. - The wide angle intra prediction mode mappingprocess as specified in clause 8.4.5.2.6 is   invoked withpredModeIntra, nTbW, nTbH and cIdx as inputs, and the modified  predModeIntra as output. - The values of the list u[ x ] with x =0..nonZeroSize − 1 are derived as follows:     xC = DiagScanOrder[ 2 ][2 ][ x ][ 0 ] (8-959)     yC = DiagScanOrder[ 2 ][ 2 ][ x ][ 1 ] (8-960)    u[ x ] = d[ xC ][ yC ]          (8-961)   - The one-dimensional lowfrequency non-separable transformation process as specified in    clause 8.7.4.2 is invoked with the input length of the scaledtransform coefficients     nonZeroSize, the transform output length nTrSset equal to nLfnstOutSize the list of scaled     non-zero transformcoefficients u[ x ] with x = 0..nonZeroSize − 1, the intra predictionmode     for LFNST set selection preModeIntra, and the LFNST index fortransform selection in the     selected LFNST set lfnst_idx[ xTbY ][yTbY ] as inputs, and the list v[ x ] with     x = 0..nLfnstOutSize − 1as output.   - The array d[ x ][ y ] with x = 0..nLfnstSize − 1, y =0..nLfnstSize − 1 is derived as follows:     - If predModeIntra is lessthan or equal to 34, the following applies:       d[ x ][ y ] = ( y < 4) ? v[ x − ( y << log2LfnstSize ) ] : (8-962)        ( ( x < 4) ? v[ 32− x − ( ( y − 4) << 2 ) ] : d[ x ][ y ] )     - Otherwise, the followingapplies:       d[ x ][ y ] = ( x < 4 ) ? v[ y − ( x << log2LfnstSize ) ]: (8-963)        ( ( y < 4) ? v[ 32 − y − ( ( x − 4) << 2 ) ] : d[ x ][y ] ) The variable implicitMtsEnabled is derived as follows: - Ifsps_mts_enabled_flag is equal to 1 and one of the following conditionsis true,   implicitMtsEnabled is set equal to 1:   -  IntraSubPartitionsSplitType is not equal to ISP_NO_SPLIT   - cu_sbt_flag is equal to 1 andMax( nTbW nTbH) is less than or equal to 32  - sps_explicit_mts_intra_enabled_flag is equal to 0 and CuPredMode[xTbY][ yTbY ] is     equal to MODE_INTRA and lfnst_idx[ x0 ][ y0 ] isequal to 0 and intra_mip_flag[ x0 ][ y0 ]     is equal to 0 - Otherwise,implicitMtsEnabled is set equal to 0. The variable trTypeHor specifyingthe horizontal transform kernel and the variable trTypeVer specifyingthe vertical transform kernel are derived as follows: - If cIdx isgreater than 0, trTypeHor and trTypeVer are set equal to 0. - Otherwise,if implicitMtsEnabled is equal to 1, the following applies:   - IfIntraSubPartitionsSplitType is not equal to ISP_NO_SPLIT or both    sps_explicit_mts_intra_enabled_flag andsps_explicit_mts_inter_enabled_flag are equal to     0 and CuPredMode[xTbY ][ yTbY] is equal to MODE_INTRA, trTypeHor and trTypeVer     arederived as follows:      trTypeHor = (nTbW >= 4 && nTbW <= 16 ) ? 1 : 0(8-964)      trTypeVer = (nTbH >= 4 && nTbH <=16) ? 1 : 0 (8-965)  - Otherwise, if cu_sbt_flag is equal to 1, trTypeHor and trTypeVer arespecified in Table 8-19     depending on cu_sbt_horizontal_flag andcu_sbt_pos_flag. - Otherwise, trTypeHor and trTypeVer are specified inTable 8-18 depending on   tu_mts_idx[ xTbY][ yTbY ]. The variablesnonZeroW and nonZeroH are derived as follows: - If lfnst_idx[ xTbY ] [yTbY ] is not equal to 0, the following applies:   nonZeroW = (nTbW == 4| nTbH = 4) ? 4 : 3   nonZeroH = (nTbW= 4 | | nTbH = 4 ) ? 4 : 8  Otherwise, the following applies:   nonZeroW = Min( nTbW, (trTypeHor > 0 ) ? 16 : 32 ) (8-966) nonZeroH = Min( nTbH, ( trTypeVer >0 ) ? 16 : 32 ) (8-967)

Table 11 shows the overall conversion process performed by the decodingapparatus.

Referring to Table 11, the variable nonZeroSize indicating the size ornumber of non-zero variables on which matrix operation is performed inorder to apply LFNST is set to 8 or 16. When the width and height of thetransform block are 4 or 8, that is, the length of the output data ofthe forward LFNST or the input data of the inverse LFNST of the 4×4block and the 8×8 block as shown in FIG. 11 is 8. For all other blocks,the length of the output data of the forward LFNST or the input data ofthe inverse LFNST is 16 [nonZeroSize=((nTbW==4 && nTbH==4)∥(nTbW==8 &&nTbH==8)) ? 8 : 16]. That is, when the forward LFNST is applied, themaximum number of output data is limited to 16.

The input data of this inverse LFNST may be two-dimensionally arrangedaccording to a diagonal scan [xC=DiagScanOrder[2][2][x][0],yC=DiagScanOrder[2][2][x][1]]. The above-described part shows thedecoding process for (i) of the LFNST simplification method.

As such, since the number of input data of the inverse LFNST for thetransform block is limited to a maximum of 16, the LFNST can be appliedto the most top-left 4×4 region in a 4×N block or a N×4 block where N is16 or more, as shown in FIG. 12 and as a result, as shown in (d) of FIG.13 , the zero-out may be performed on the remaining blocks to which the4×4 LFNST is not applied.

On the other hand, when the intra prediction mode is greater than orequal to 81, that is, when CCLM is applied during the intra predictionof the chroma block, an intra prediction mode (predModeIntra) forderiving a transform set may be set as an intra mode(IntraPredModeY[xTbY+nTbW/2][yTbY+nTbH/2]) of a corresponding lumablock.

Meanwhile, a variable implicitMtsEnabled indicating whether the MTS isimplicitly performed may be set to 1 when it satisfies the conditionsthat flag information sps_mts_enabled_flag signaled at the sequenceparameter level is 1, sps_explicit_mts_intra_enabled_flag is 0, theintra prediction mode is applied to the current block, lfnst_idx is 0,and intra_mip_flag is 1.

In addition, variables nonZeroW and nonZeroH indicating the width andheight of the upper-left block in which the non-zero transformcoefficient input to the inverse primary transform can exist are isderived as 4 when the lfnst index is not 0 and the width or width of thetransform block is 4, otherwise is derived as 8[nonZeroW=(nTbW==4∥nTbH==4) ? 4 : 8, nonZeroH=(nTbW==4∥nTbH==4) ? 4 :8]. That is, in the transform block, the zero-out is performed in theregions other than the 4×4 region and the 8×8 region to which the lfnstis applied. This part shows the decoding process for (ii) of the LFNSTsimplification method.

TABLE 12 8.7.4.3 Low frequency non-separable transformation matrixderivation process Inputs to this process are: - a variable nTrSspecifying the transform output length, - a variable predModeIntraspecifying the intra prediction mode for LFNST set selection, - avariablelfnstidx specifying the LFNST index for transform selection inthe selected LFNST  set. Output of this process is the transformationmatrix lowFreqTransMatrix. The variable lfnstTrSetIdx is specified inTable 8-20 - Specification of lfnstTrSetIdx depending on predModeIntra.Table 8-20 - Specification of lfnstTrSetIdx predModeIntra lfnstTrSetIdxpredModeIntra < 0 1 0 <= predModeIntra <= 1 0  2 <= predModeIntra <= 121 13 <= predModeIntra <= 23 2 24 <= predModeIntra <= 44 3 45 <=predModeIntra <= 55 2 56 <= predModeIntra <= 80 1

Table 12 shows a transform set for the LFNST and an LFNST transform setderived based on an input value for deriving a transform kernel matrixand an intra prediction mode.

As shown in Table 12, the transform kernel matrix (lowFreqTransMatrix)can be derived using a variable nTrS indicating the transform outputsize to derive the transform kernel matrix, intra prediction modeinformation (predModeIntra) for selection of the LFNST transform set,and the LFNST index signaled from the coding unit as input values.

There are four LFNST transform sets, such as 0, 1, 2, and 3, and thesame transform set can be applied to modes located in mutually symmetricdirections based on the symmetry of the intra prediction mode. When theintra prediction mode is non-directional planar mode or DC mode(0<=predModeIntra<=1), then the transform set is 0, in the case ofwide-angle intra prediction mode (predModeIntra<0,56<=predModeIntra<=80), the transform set is 1.

On the other hand, as described above, when the CCLM is applied to thechroma block, the intra prediction mode (predModeIntra) of the chromablock for deriving the transform set can be set to the intra mode of thecorresponding luma block (IntraPredModeY[xTbY+nTbW/2][yTbY+nTbH/2])rather than 81 to 83 indicating the CCLM or the planar mode.

Accordingly, 81 to 83 are omitted in the intra prediction mode(predModeIntra) for transform set selection of Table 12.

Meanwhile, Table 13 below shows ctxInc allocated to the bin index of thetu_mts_idx syntax element described above (Assignment of ctxInc tosyntax elements with context coded bins).

TABLE 13 binIdx Syntax element 0 1 2 3 4 >=5 . . . . . . . . . . . . . .. . . . . . . tu_cbf_cr[ ][ ][ ] tu_cbf_cb[ ][ ][ ] na na na na nacu_qp_delta_abs 0 1 1 1 1 bypass cu_qp_delta_sign_flag bypass na na nana na transform_skip_flag[ ][ ] 0 na na na na na tu_mts_idx[ ][ ] 0 1 23 na na tu_joint_cbcr_residual[ ][ ] 0 na na na na na

As shown in Table 13, ctxInc of the first bin (binIdx=0) of tu_mts_idxis 0, ctxInc of the second bin (binIdx=1) is 1, and ctxInc of the thirdbin (binIdx=2) is 2 and the fourth ctxInc of a bin (binIdx=3) is 3.

In the conventional case, any one ctxInc is selected from among aplurality of ctxInc according to a predetermined condition and allocatedto the first bin, as described above, by allocating one fixed ctxInc tothe first bin without complying with a specific condition, codingefficiency can be increased.

The following drawings are provided to describe specific examples of thepresent disclosure. Since the specific designations of devices or thedesignations of specific signals/messages/fields illustrated in thedrawings are provided for illustration, technical features of thepresent disclosure are not limited to specific designations used in thefollowing drawings.

FIG. 16 is a flowchart illustrating an operation of a video decodingapparatus according to an embodiment of the present disclosure.

Each operation illustrated in FIG. 16 may be performed by the decodingapparatus 300 illustrated in FIG. 3 . Specifically, S1610 to S1650 maybe performed by the entropy decoder 310 illustrated in FIG. 3 , S1620may be performed by the dequantizer 321 illustrated in FIGS. 3 , S1660and S1670 may be performed by the inverse transformer 322 illustrated inFIGS. 3 and S1680 may be performed by the adder 340 illustrated in FIG.3 . Operations according to S1610 to S1680 are based on some of theforegoing details explained with reference to FIG. 4 to FIG. 15 .Therefore, a description of specific details overlapping with thoseexplained above with reference to FIG. 3 to FIG. 15 will be omitted orwill be made briefly.

The decoding apparatus 300 according to an embodiment receives abitstream including residual information, and may derive residualinformation about a current block, that is, a transform block to betransformed, eg, quantized transform coefficients, from the bitstream(S1610).

More specifically, the decoding apparatus 300 may decode information onquantized transform coefficients for the target block from the bitstreamand may derive the quantized transform coefficients for the currentblock based on the information on the quantized transform coefficientsfor the current block. The information on the quantized transformcoefficients for the target block may be included in a sequenceparameter set (SPS) or a slice header and may include at least one ofinformation on whether a reduced transform (RST) is applied, informationon the simplification factor, information on a minimum transform size inwhich the reduced transform is applied, information on a maximumtransform size in which the reduced transform is applied, a reducedinverse transform size, and information on a transform index indicatingany one of transform kernel matrices included in a transform set.

The decoding apparatus 300 may perform dequantization on the quantizedtransform coefficients of the current block to derive transformcoefficients (S1620).

The derived transform coefficients may be two-dimensionally arranged inthe current block, and the decoding apparatus may derive the non-zerodata, ie, information on non-zero significant coefficients in thecurrent block, through the residual coding. That is, the decodingapparatus may determine the last position information of the non-zerosignificant coefficient in the current block.

The transform coefficients derived based on the residual information ofS1620 may be the dequantized transform coefficients as described above,or may be quantized transform coefficients. That is, the transformcoefficients may be data capable of checking whether the non-zero datain the current block regardless of quantization or not.

The decoding apparatus may derive a first variable indicating whether asignificant coefficient exists in a region other than a DC region (aregion in which a DC component is located) of at least one transformblock among transform blocks constituting the coding block (S1630).

In this document, according to an example, the DC region may mean only aposition with respect to a DC transform coefficient, that is, only atop-left position of a transform block.

The first variable may be a variable LfnstDcOnly that may be derived ina residual coding process. The first variable may be derived as 0 whenthe index of the subblock including the last significant coefficient inthe current block is 0 and the position of the last significantcoefficient in the subblock is greater than 0, and if the first variableis 0, the LFNST index can be parsed.

The first variable may be initially set to 1, and may be maintained at 1or may be changed to 0 depending on whether the significant coefficientexists in the region other than the DC region.

According to an example, a variable log 2SbW and a variable log 2SbHindicating the height and width of the sub-block may be derived based onthe size of the transform block, and numSbCoeff representing the numberof coefficients that may exist in the subblock may be set based on thevariable log 2SbW and the variable log 2SbH [numSbCoeff=1<<(log 2SbW30log 2SbH)].

The variable lastScanPos indicating the position of the last significantcoefficient within the subblock is initially set to numSbCoeff, and thevariable lastSubBlock indicating the subblock in which the last non-zerocoefficient exists is initially “(1<<(log 2TbWidth+log 2TbHeight−(log2SbW+log 2SbH)))−set to 1”

While scanning in the diagonal direction in the subblock correspondingto lastSubBlock [lastScanPos−−], it is checked whether the lastsignificant coefficient other than 0 exists at the correspondingposition.

when a significant coefficient is not found until the variablelastScanPos becomes 0 within the subblock pointed to by lastSubBlock,the variable lastScanPos is set to numSbCoeff again, and the variablelastSubBlock is also changed to the next sub-block in the scan direction[lastSubBlock−−].

That is, as the variable lastScanPos and the variable lastSubBlock areupdated according to the scan direction, the position where the lastnon-zero coefficient exists is identified.

The variable LfnstDcOnly indicates whether a non-zero coefficient existsat a position that is not a DC component for at least one transformblock in one coding unit, when the non-zero coefficient exists in theposition that is not the DC component for at least one transform blockin the one coding unit, it becomes 0, and when non-zero coefficients donot exist at positions other than the DC components for all transformblocks in the one coding unit it becomes 1.

As shown in Table 8, when the index of the subblock in which the lastnon zero coefficient exists is 0 [lastSubBlock==0], and the position ofthe last nonzero coefficient in the subblock is greater than 0[lastScanPos>0], the variable LfnstDcOnly may be derived as 0. Thevariable LfnstDcOnly can be derived as 0 only when the width and heightof the transform block are 4 or more [log 2TbWidth>=2 && log2TbHeight>=2], and no transform skip is applied[!transform_skip_flag[x0][y0]].

According to an example, the decoding apparatus may derive a secondvariable indicating whether a significant coefficient exists in thesecond region other than the first region at top-left of the currentblock (S1640).

The second variable may be a variable LfnstZeroOutSigCoeffFlag that mayindicate that zero-out is performed when the LFNST is applied. Thesecond variable is initially set to 1, and when a significantcoefficient exists in the second region, the second variable may bechanged to 0.

The variable LfnstZeroOutSigCoeffFlag can be derived as 0 when the indexof the subblock in which the last non-zero coefficient exists is greaterthan 0 and the width and height of the transform block are both greaterthan 4 [(lastSubBlock>0 && log 2TbWidth>=2 && log 2TbHeight>=2)], orwhen the last position of the non-zero coefficient within the subblockin which the last non-zero coefficient exists is greater than 7 and thesize of the transform block is 4×4 or 8×8 [(lastScanPos>7 && (log2TbWidth==2 log 2TbHeight==3) && log 2TbWidth==log 2TbHeight)].

That is, in the transform block, when non-zero coefficients are derivedfrom regions other than the top-left region where LFNST transformcoefficients can exist, or for 4×4 blocks and 8×8 blocks when thenon-zero coefficient exists outside the 8th position in the scan order,the variable LfnstZeroOutSigCoeffFlag is set to 0.

The first region may be derived based on the size of the current block.

For example, when the size of the current block is 4×4 or 8×8, the firstregion may be from the top-left of the current block to the eighthsample position in the scan direction.

When the size of the current block is 4×4 or 8×8, since 8 data areoutput through the forward LFNST, the 8 transform coefficients receivedby the decoding apparatus can be arranged from the top-left of thecurrent block to the 8th sample position in the scan direction as inFIG. 13(a) and FIG. 14(a).

Also, when the size of the current block is not 4×4 or 8×8, the firstregion may be a 4×4 area at the top-left of the current block. If thesize of the current block is not 4×4 or 8×8, since 16 data are outputthrough the forward LFNST, 16 transform coefficients received by thedecoding apparatus may be arranged in the top-eft 4×4 area of thecurrent block as shown in FIGS. 13(b) to (d) and FIG. 14(b).

Meanwhile, transform coefficients that may be arranged in the firstregion may be arranged along a diagonal scan direction as shown in FIG.8 .

Also, according to an example, the maximum number of transformcoefficients that may exist in a block to which the LFNST is applied maybe 16.

When the first variable indicates that the significant coefficientexists in the region other than the DC region, and the second variableindicates that there is no significant coefficient in the second region,the decoding apparatus can parse the LFNST index from the bitstream(S1650).

That is, when the first variable that was set to 1 is changed to 0 andthe second variable is maintained at 1, the LFNST index may be parsed.In other words, there is the significant coefficient in the sub-blockincluding the DC region, that is, the top-left 4×4 block, in addition tothe DC region, and when the significant coefficient does not exist bychecking the significant coefficient up to the second region of thecurrent block, the LFNST index for the LFNST may be parsed.

In summary, at the coding unit level, the first variable LfnstDcOnly andthe second variable LfnstZeroOutSigCoeffFlag are set to 1, respectively,and then are newly derived through the process shown in Table 8 at theresidual coding level. Only when the variable LfnstDcOnly derived fromthe residual coding level is 0 and the variable LfnstZeroOutSigCoeffFlagis 1 [if(LfnstDcOnly==0 && LfnstZeroOutSigCoeffFlag==1), lfnst_idx maybe signaled at the coding unit level.

As described above, when the forward LFNST is performed by the encodingapparatus, the zero-out in which the remaining regions of the currentblock except for the region in which the LFNST transform coefficientsmay exist may be performed as 0.

Therefore, when the significant coefficient exists in the second region,it is certain that the LFNST is not applied, so the LFNST index is notsignaled and the decoding apparatus does not parse the LFNST index.

The LFNST index information is received as syntax information and thesyntax information is received as a binarized bin string including 0 and1.

The syntax element of the LFNST index according to this embodiment mayindicate whether an inverse LFNST or an inverse non-separable transformis applied and any one of a transform kernel matrix included in thetransform set, and the transform set includes two transform kernelmatrices. In this case, the syntax element of the transform index mayhave three values.

That is, according to an embodiment, the syntax element value for theLFNST index may be include 0 indicating a case in which the inverseLFNST is not applied to the target block, 1 indicating the firsttransformation kernel matrix among the transformation kernel matrices,and 2 indicating the second transform kernel matrix among thetransformation kernel matrices.

When the LFNST index is parsed, the decoding apparatus may apply theLFNST matrix to the transform coefficients of the first region to derivemodified transform coefficients (S1660).

The inverse transformer 332 of the decoding apparatus 300 may determinea transform set based on a mapping relationship according to an intraprediction mode applied to a current block, and may perform an inverseLFNST, that is, the inverse non-separable transformation based on thetransform set and the values of syntax elements for the LFNST index.

As described above, a plurality of transform sets may be determinedaccording to an intra prediction mode of a transform block to betransformed, and an inverse LFNST may be performed based on any one oftransform kernel matrices, that is, LFNST matrices included in atransform set indicated by an LFNST index. A matrix applied to theinverse LFNST may be named as an inverse LFNST matrix or an LFNSTmatrix, and the name of this matrix is irrelevant as long as it has atranspose relation with the matrix used for the forward LFNST.

In one example, the inverse LFNST matrix may be a non-square matrix inwhich the number of columns is less than the number of rows.

Meanwhile, a predetermined number of modified transform coefficients maybe derived based on the size of the current block. For example, when theheight and width of the current block are 8 or more, 48 modifiedtransform coefficients are derived as shown on the left of FIG. 7 . Andwhen the width and height of the current block are not equal to orgreater than 8, that is, when the width and height of the current blockare greater than or equal to 4 and the width or height of the currentblock is less than 8, 16 modified transform coefficients may be derivedas shown on the right of FIG. 7 .

As shown in FIG. 7 , the 48 modified transform coefficients may bearranged in the top-left, top-right, and bottom-left 4×4 regions of thetop-left 8×8 region of the current block, and the 16 modified transformcoefficients may be arranged in the top-left 4×4 region of the currentblock.

The 48 modified transform coefficients and the 16 modified transformcoefficients may be arranged in a vertical or horizontal directionaccording to the intra prediction mode of the current block. Forexample, when the intra prediction mode is a horizontal direction (modes2 to 34 in FIG. 9 ) based on a diagonal direction (mode 34 in FIG. 9 ),the modified transform coefficients may be arranged in the horizontaldirection, that is, in the row-first direction, as shown in (a) of FIG.7 . When the intra prediction mode is a vertical direction (modes 35 to66 in FIG. 9 ) based on a diagonal direction, the modified transformcoefficients may be arranged in the vertical direction, that is, in acolumn-first direction, as shown in (b) of FIG. 7 .

In one embodiment, S1660 may include decoding the transform index,determining whether it corresponds to the conditions to apply theinverse RST based on the transform index, that is, the LFNST index,selecting a transform kernel matrix and applying the inverse LFNST tothe transform coefficients based on the selected transform kernel matrixand/or the simplification factor when the conditions for applying theinverse LFNST is satisfied. In this case, the size of the simplificationinverse transform matrix may be determined based on the simplificationfactor.

Referring to S1660, it can be confirmed that residual samples for thetarget block are derived based on the inverse LFNST of the transformcoefficients for the target block. Regarding the size of an inversetransform matrix, the size of a general inverse transform matrix is N×N,while the size of an inverse LFNST matrix is reduced to N×R, thus makingit possible to reduce memory occupancy by an R/N ratio when performingthe inverse LFNST compared to when performing a general transform.Further, compared to the number of multiplication operations, N×N, whenusing the general inverse transform matrix, it is possible to reduce thenumber of multiplication operations by an R/N ratio (to N×R) when theinverse LFNST matrix is used. In addition, since only R transformcoefficients need to be decoded when the inverse LFNST is applied, thetotal number of transform coefficients for the target block may bereduced from N to R, compared to when the general inverse transform isapplied in which N transform coefficients need to be decoded, thusincreasing decoding efficiency. That is, according to S1660, (inverse)transform efficiency and decoding efficiency of the decoding apparatus300 may be increased through the inverse LFNST.

The decoding apparatus 300 according to an embodiment may deriveresidual samples for the target block based on the inverse primarytransform of the modified transform coefficients (S1670).

On the other hand, when the LFNST is not applied, only the MTS-basedprimary inverse transform procedure may be applied in the inversetransform procedure as follows. That is, the decoding apparatus maydetermine whether the LFNST is applied to the current block as in theabove-described embodiment, and when the LFNST is not applied, thedecoding apparatus may derive residual samples from transformcoefficients through a primary inverse transform.

The decoding apparatus may determine that the LFNST is not applied whensignificant coefficients exist in the second region other than the firsttop-left region of the current block, and may derive residual samplesfrom the transform coefficients through primary inverse transform.

The primary inverse transform procedure may be referred to as an inverseprimary transform procedure or an inverse MTS transform procedure. Suchan MTS-based primary inverse transform procedure may also be omitted insome cases.

In addition, a simplified inverse transform may be applied to theinverse primary transform, or a conventional separable transform may beused.

The decoding apparatus 300 according to an embodiment may generatereconstructed samples based on residual samples of the current block andprediction samples of the current block (S1680).

The following drawings are provided to describe specific examples of thepresent disclosure. Since the specific designations of devices or thedesignations of specific signals/messages/fields illustrated in thedrawings are provided for illustration, technical features of thepresent disclosure are not limited to specific designations used in thefollowing drawings.

FIG. 17 is a flowchart illustrating an operation of a video encodingapparatus according to an embodiment of the present disclosure.

Each operation illustrated in FIG. 17 may be performed by the encodingapparatus 200 illustrated in FIG. 2 . Specifically, S1710 may beperformed by the predictor 220 illustrated in FIG. 2 , S1720 may beperformed by the subtractor 231 illustrated in FIGS. 2 , S1730 to S1750may be performed by the transformer 232 illustrated in FIGS. 2 , andS1760 and S1770 may be performed by the quantizer 233 and the entropyencoder 240 illustrated in FIG. 2 . Operations according to S1710 toS1770 are based on some of contents described in FIG. 4 to FIG. 15 .Therefore, a description of specific details overlapping with thoseexplained above with reference to FIG. 2 and FIG. 4 to FIG. 15 will beomitted or will be made briefly.

The encoding apparatus 200 according to an embodiment may deriveprediction samples based on the intra prediction mode applied to thecurrent block (S1710).

The encoding apparatus 200 according to an embodiment may deriveresidual samples for the current block based on the prediction samples(S1720).

The encoding apparatus 200 according to an embodiment may derivetransform coefficients for the target block based on a primary transformfor the residual samples (S1730).

The primary transform may be performed through a plurality of transformkernels, and in this case, a transform kernel may be selected based onthe intra prediction mode.

The encoding apparatus 200 may determine whether to perform a secondarytransform or a non-separable transform, specifically, LFNST, ontransform coefficients for the current block .

When it is determined to perform the LFNST, the encoding apparatus 200may derive modified transform coefficients for the current block basedon the transform coefficients of the first region at the top-left of thecurrent block and a predetermined LFNST matrix (S1740).

The encoding apparatus 200 may determine a transform set based on amapping relationship according to an intra prediction mode applied to acurrent block, and may perform the LFNST, that is, a non-separabletransform based on one of two LFNST matrices included in the transformset.

As described above, a plurality of transform sets may be determinedaccording to the intra prediction mode of a transform block to betransformed. A matrix applied to the LFNST has a transpose relationshipwith a matrix used for the inverse LFNST.

In one example, the LFNST matrix may be a non-square matrix in which thenumber of rows is less than the number of columns.

The first region may be derived based on the size of the current block.For example, when the height and width of the current block is greaterthan or equal to 8, the first region is a 4×4 area of the top-left,top-right, and bottom-left of the 8×8 area at the top-left of thecurrent block as shown in the left of FIG. 7 . When the height and widthof the current block are not equal to or greater than 8, the firstregion may be a 4×4 area at the top-left of the current block as shownin the right of FIG. 7 .

The transform coefficients of the first region may be one-dimensionallyarranged in a vertical or horizontal direction according to the intraprediction mode of the current block for a multiplication operation withthe LFNST matrix.

The 48 modified transform coefficients or the 16 modified transformcoefficients of the first region may be read in the vertical orhorizontal direction according to the intra prediction mode of thecurrent block and arranged in one dimension. For example, if the intraprediction mode is a horizontal direction (modes 2 to 34 in FIG. 9 )based on a diagonal direction (mode 34 in FIG. 9 ), the transformcoefficients may be arranged in the horizontal direction, that is, inthe row-first direction, as shown in (a) of FIG. 7 . When the intraprediction mode is a vertical direction (modes 35 to 66 in FIG. 9 )based on the diagonal direction, the transform coefficients may bearranged in the vertical direction, that is, in a column-firstdirection, as shown in (b) of FIG. 7 .

In one example, the LFNST may be performed based on a simplifiedtransform matrix or a transform kernel matrix, and the simplifiedtransform matrix may be a non-square matrix in which the number of rowsis less than the number of columns.

In one embodiment, S1740 may include determining whether the conditionsfor applying the LFNST are satisfied, generating and encoding the LFNSTindex based on the determination, selecting a transform kernel matrixand applying the LFNST to residual samples based on the selectedtransform kernel matrix and/or the simplification factor when theconditions for applying LFNST is satisfied. In this case, the size ofthe simplification transform matrix may be determined based on thesimplification factor.

Referring to S1740, it can be confirmed that transform coefficients forthe target block are derived based on the LFNST for the residualsamples. Regarding the size of a transform kernel matrix, the size of ageneral transform kernel matrix is N×N, while the size of a simplifiedtransform matrix is reduced to R×N, thus making it possible to reducememory occupancy by an R/N ratio when performing the RST compared towhen performing a general transform. Further, compared to the number ofmultiplication operations, N×N, when using the general transform kernelmatrix, it is possible to reduce the number of multiplication operationsby an R/N ratio (to R×N) when the simplified transform kernel matrix isused. In addition, since only R transform coefficients are derived whenthe RST is applied, the total number of transform coefficients for thetarget block may be reduced from N to R, compared to when the generaltransform is applied in which N transform coefficients are derived, thusreducing the amount of data transmitted by the encoding apparatus 200 tothe decoding apparatus 300. That is, according to S1740, transformefficiency and coding efficiency of the encoding apparatus 200 may beincreased through the LFNST.

Meanwhile, according to an example, the encoding apparatus may zero outthe second region of the current block in which the modified transformcoefficients do not exist (S1750).

As FIGS. 13 and 14 , all remaining regions of the current block in whichthe modified transform coefficients do not exist may be treated aszeros. Due to the zero-out, the amount of computation required toperform the entire transform process is reduced, and the amount ofcomputation required for the entire transform process is reduced,thereby reducing power consumption required to perform the transform. Inaddition, the image coding efficiency may be increased by reducing thelatency involved in the transform process.

On the other hand, when the LFNST is not applied, only the MTS-basedprimary transform procedure may be applied in the transform procedure asdescribed above. That is, the encoding apparatus may determine whetherthe LFNST is applied to the current block as in the above-describedembodiment, and when the LFNST is not applied, the encoding apparatusmay derive transform coefficients from residual samples through theprimary transform.

This primary transform procedure may be referred to as a primarytransform procedure or an MTS transform procedure. Such an MTS-basedprimary transform procedure may also be omitted in some cases.

The encoding apparatus according to an example may configure imageinformation such that an LFNST index indicating an LFNST matrix isparsed when a significant coefficient exists in a region excluding a DCregion of the current block and the above-described zero-out isperformed (S1760).

The encoding apparatus may configure the image information so that theimage information shown in Tables 6 and 8 may be parsed by the decodingapparatus.

According to an example, when the index of the subblock including thelast significant coefficient in the current block is 0 and the positionof the last significant coefficient in the subblock is greater than 0,it is determined that the significant coefficient exists in the regionother than the DC region, and the image information can be configuredsuch that the LFNST index is signaled. In this document, the firstposition in the scan order may be 0.

In addition, according to an example, when the index of the sub-blockincluding the last significant coefficient in the current block isgreater than 0 and the width and height of the current block are 4 ormore, it is determined that it is certain that the LFNST is not applied,and the image information may be configured so that the LFNST index isnot signaled.

In addition, according to an example, when the size of the current blockis 4×4 or 8×8 and the start of the position in the scan order is 0, theposition of the last significant coefficient is greater than 7, theencoding apparatus may determine that it is certain that the LFNST isnot applied, and configure the image information so that the LFNST indexis not signaled.

That is, the encoding apparatus can configure the image information sothat the LFNST index can be parsed according to the derived variablevalue after the variable LfnstDcOnly and the variableLfnstZeroOutSigCoeffFlag are derived in the decoding apparatus.

The encoding apparatus 200 according to an embodiment may derivequantized transform coefficients by performing quantization based on themodified transform coefficients for the target block, and may encode andoutput image information including information about the quantizedtransform coefficients and the LFNST index (S1770).

That is, the encoding apparatus may generate residual informationincluding information on quantized transform coefficients. The residualinformation may include the above-described transform relatedinformation/syntax element. The encoding apparatus may encodeimage/video information including residual information and output theencoded image/video information in the form of a bitstream.

More specifically, the encoding apparatus 200 may generate informationabout the quantized transform coefficients and encode the informationabout the generated quantized transform coefficients.

In one example, information on the quantized transform coefficients mayinclude at least one of information on whether LFNST is applied,information on a simplification factor, information on a minimumtransform size to which LFNST is applied, and information on a maximumtransform size to which LFNST is applied.

Also, the encoding apparatus 200 may encode information on the size ofthe maximum transform applied block, for example, syntax information onthe transform block size such as 3sps_log2_max_luma_transform_size_minus5, or flag information such assps_max_luma_transform_size_64_flag at the sequence parameter set level.

In the present disclosure, at least one of quantization/dequantizationand/or transform/inverse transform may be omitted. Whenquantization/dequantization is omitted, a quantized transformcoefficient may be referred to as a transform coefficient. Whentransform/inverse transform is omitted, the transform coefficient may bereferred to as a coefficient or a residual coefficient, or may still bereferred to as a transform coefficient for consistency of expression.

In addition, in the present disclosure, a quantized transformcoefficient and a transform coefficient may be referred to as atransform coefficient and a scaled transform coefficient, respectively.In this case, residual information may include information on atransform coefficient(s), and the information on the transformcoefficient(s) may be signaled through a residual coding syntax.Transform coefficients may be derived based on the residual information(or information on the transform coefficient(s)), and scaled transformcoefficients may be derived through inverse transform (scaling) of thetransform coefficients. Residual samples may be derived based on theinverse transform (transform) of the scaled transform coefficients.These details may also be applied/expressed in other parts of thepresent disclosure.

In the above-described embodiments, the methods are explained on thebasis of flowcharts by means of a series of steps or blocks, but thepresent disclosure is not limited to the order of steps, and a certainstep may be performed in order or step different from that describedabove, or concurrently with another step. Further, it may be understoodby a person having ordinary skill in the art that the steps shown in aflowchart are not exclusive, and that another step may be incorporatedor one or more steps of the flowchart may be removed without affectingthe scope of the present disclosure.

The above-described methods according to the present disclosure may beimplemented as a software form, and an encoding apparatus and/ordecoding apparatus according to the disclosure may be included in adevice for image processing, such as, a TV, a computer, a smartphone, aset-top box, a display device or the like.

When embodiments in the present disclosure are embodied by software, theabove-described methods may be embodied as modules (processes, functionsor the like) to perform the above-described functions. The modules maybe stored in a memory and may be executed by a processor. The memory maybe inside or outside the processor and may be connected to the processorin various well-known manners. The processor may include anapplication-specific integrated circuit (ASIC), other chipset, logiccircuit, and/or a data processing device. The memory may include aread-only memory (ROM), a random access memory (RAM), a flash memory, amemory card, a storage medium, and/or other storage device. That is,embodiments described in the present disclosure may be embodied andperformed on a processor, a microprocessor, a controller or a chip. Forexample, function units shown in each drawing may be embodied andperformed on a computer, a processor, a microprocessor, a controller ora chip.

Further, the decoding apparatus and the encoding apparatus to which thepresent disclosure is applied, may be included in a multimediabroadcasting transceiver, a mobile communication terminal, a home cinemavideo device, a digital cinema video device, a surveillance camera, avideo chat device, a real time communication device such as videocommunication, a mobile streaming device, a storage medium, a camcorder,a video on demand (VoD) service providing device, an over the top (OTT)video device, an Internet streaming service providing device, athree-dimensional (3D) video device, a video telephony video device, anda medical video device, and may be used to process a video signal or adata signal. For example, the over the top (OTT) video device mayinclude a game console, a Blu-ray player, an Internet access TV, a Hometheater system, a smartphone, a Tablet PC, a digital video recorder(DVR) and the like.

In addition, the processing method to which the present disclosure isapplied, may be produced in the form of a program executed by acomputer, and be stored in a computer-readable recording medium.Multimedia data having a data structure according to the presentdisclosure may also be stored in a computer-readable recording medium.The computer-readable recording medium includes all kinds of storagedevices and distributed storage devices in which computer-readable dataare stored. The computer-readable recording medium may include, forexample, a Blu-ray Disc (BD), a universal serial bus (USB), a ROM, aPROM, an EPROM, an EEPROM, a RAM, a CD-ROM, a magnetic tape, a floppydisk, and an optical data storage device. Further, the computer-readablerecording medium includes media embodied in the form of a carrier wave(for example, transmission over the Internet). In addition, a bitstreamgenerated by the encoding method may be stored in a computer-readablerecording medium or transmitted through a wired or wirelesscommunication network. Additionally, the embodiments of the presentdisclosure may be embodied as a computer program product by programcodes, and the program codes may be executed on a computer by theembodiments of the present disclosure. The program codes may be storedon a computer-readable carrier.

FIG. 18 illustrates the structure of a content streaming system to whichthe present disclosure is applied.

Further, the contents streaming system to which the present disclosureis applied may largely include an encoding server, a streaming server, aweb server, a media storage, a user equipment, and a multimedia inputdevice.

The encoding server functions to compress to digital data the contentsinput from the multimedia input devices, such as the smart phone, thecamera, the camcoder and the like, to generate a bitstream, and totransmit it to the streaming server. As another example, in a case wherethe multimedia input device, such as, the smart phone, the camera, thecamcoder or the like, directly generates a bitstream, the encodingserver may be omitted. The bitstream may be generated by an encodingmethod or a bitstream generation method to which the present disclosureis applied. And the streaming server may store the bitstream temporarilyduring a process to transmit or receive the bitstream.

The streaming server transmits multimedia data to the user equipment onthe basis of a user's request through the web server, which functions asan instrument that informs a user of what service there is. When theuser requests a service which the user wants, the web server transfersthe request to the streaming server, and the streaming server transmitsmultimedia data to the user. In this regard, the contents streamingsystem may include a separate control server, and in this case, thecontrol server functions to control commands/responses betweenrespective equipments in the content streaming system.

The streaming server may receive contents from the media storage and/orthe encoding server. For example, in a case the contents are receivedfrom the encoding server, the contents may be received in real time. Inthis case, the streaming server may store the bitstream for apredetermined period of time to provide the streaming service smoothly.

For example, the user equipment may include a mobile phone, a smartphone, a laptop computer, a digital broadcasting terminal, a personaldigital assistant (PDA), a portable multimedia player (PMP), anavigation, a slate PC, a tablet PC, an ultrabook, a wearable device(e.g., a watch-type terminal (smart watch), a glass-type terminal (smartglass), a head mounted display (HMD)), a digital TV, a desktop computer,a digital signage or the like. Each of servers in the contents streamingsystem may be operated as a distributed server, and in this case, datareceived by each server may be processed in distributed manner.

Claims disclosed herein can be combined in a various way. For example,technical features of method claims of the present disclosure can becombined to be implemented or performed in an apparatus, and technicalfeatures of apparatus claims can be combined to be implemented orperformed in a method. Further, technical features of method claims andapparatus claims can be combined to be implemented or performed in anapparatus, and technical features of method claims and apparatus claimscan be combined to be implemented or performed in a method.

1-15. (canceled)
 16. An image decoding method performed by a decodingapparatus, the method comprising: obtaining residual information from abitstream; deriving transform coefficients for a current block based onthe residual information; determining whether a Low FrequencyNon-Separable Transform (LFNST) index is parsed; parsing the LFNST indexbased on the determination that the LFNST index is parsed; derivingmodified transform coefficients by applying an LFNST matrix derivedbased on the LFNST index to the transform coefficients in the firstregion; deriving residual samples for the current block based on aninverse primary transform for the modified transform coefficients; andgenerating a reconstructed picture based on the residual samples for thecurrent block, wherein the determining whether the LFNST index is parsedcomprising: deriving a first variable related to whether a significantcoefficient exists in a region excluding a Direct-Current (DC) region ofthe current block; deriving a second variable related to whether thesignificant coefficient exists in a second region other than a firstregion at a top-left of the current block; wherein the first variable isderived as 0 based on an index of a subblock including a lastsignificant coefficient in the current block being 0 and a position ofthe last significant coefficient in the subblock being greater than 0,and wherein the LFNST index is parsed based on the first variable being0 and the second variable being related to that the significantcoefficient does not exist in the second region.
 17. The image decodingmethod of claim 16, wherein the first region is derived based on a sizeof the current block, wherein based on the size of the current blockbeing 4×4 or 8×8, the first region is from the top-left of the currentblock to an 8th sample position in a scan direction, and wherein basedon the size of the current block not being 4×4 or 8×8, the first regionis a 4×4 area at the top-left of the current block.
 18. The imagedecoding method of claim 16, wherein a predetermined number of themodified transform coefficients are derived based on a size of thecurrent block, wherein based on a height and a width of the currentblock being greater than or equal to 8, 48 modified transformcoefficients are derived, and wherein based on the width and the heightof the current block being 4 or more and the width or the height of thecurrent block is less than 8, 16 modified transform coefficients arederived.
 19. An image encoding method performed by an image encodingapparatus, the method comprising: deriving prediction samples for acurrent block; deriving residual samples for the current block based onthe prediction samples; deriving transform coefficients for the currentblock based on a primary transform for the residual samples; derivingmodified transform coefficients for the current block based on thetransform coefficients of a first region at a top-left of the currentblock and a predetermined Low Frequency Non-Separable Transform (LFNST)matrix; constructing image information so that an LFNST index related tothe LFNST matrix is signaled based on a significant coefficient existingin a region excluding a Direct-Current (DC) region of the current blockand the significant coefficient existing in a second region other than afirst region at a top-left of the current block, and encoding the imageinformation including residual information derived through quantizationof the modified transform coefficients and the LFNST index, whereinbased on an index of a subblock including a last significant coefficientin the current block being 0 and a position of the last significantcoefficient in the subblock being greater than 0, it is determined thatthe significant coefficient exists in the region excluding the DCregion, and the image information is configured such that the LFNSTindex is signaled.
 20. The image encoding method of claim 19, whereinthe first region is derived based on a size of the current block,wherein based on a height and a width of the current block being greaterthan or equal to 8, the first region is a top-left, a top-right, and abottom-left 4×4 areas within a top-left 8×8 area of the current block,and wherein based on the width and the height of the current block being4 or more and the width or the height of the current block being lessthan 8, the first region is the top-left 4×4 area of the current block.21. The image encoding method of claim 19, wherein a predeterminednumber of the modified transform coefficients are derived based on asize of the current block, wherein based on the size of the currentblock being 4×4 or 8×8, 8 modified transform coefficients are derived,and wherein based on the size of the current block not being 4×4 or 8×8,16 modified transform coefficients are derived.
 22. A non-transitorycomputer-readable storage medium storing a bitstream generated by theimage encoding method of claim
 19. 23. A transmission method of data foran image, the method comprising: obtaining a bitstream for the image,wherein the bitstream is generated based on deriving prediction samplesfor a current block; deriving residual samples for the current blockbased on the prediction samples; deriving transform coefficients for thecurrent block based on a primary transform for the residual samples;deriving modified transform coefficients for the current block based onthe transform coefficients of a first region at a top-left of thecurrent block and a predetermined Low Frequency Non-Separable Transform(LFNST) matrix; constructing image information so that an LFNST indexrelated to the LFNST matrix is signaled based on a significantcoefficient existing in a region excluding a Direct-Current (DC) regionof the current block and the significant coefficient existing in asecond region other than a first region at a top-left of the currentblock, and encoding the image information including residual informationderived through quantization of the modified transform coefficients andthe LFNST index to generate the bitsream, and transmitting the datacomprising the bitstream, wherein based on an index of a subblockincluding a last significant coefficient in the current block being 0and a position of the last significant coefficient in the subblock beinggreater than 0, it is determined that the significant coefficient existsin the region excluding the DC region, and the image information isconfigured such that the LFNST index is signaled.